UPDATE:

I've been trying a few things and it seems like the trigger is working ok if I modify the inventoryitem object form the standard SF edit page.  But the recordtype change to lock isn't working when the inventoryitem objects are modified from a controller extension.  

Here is the code for my controller extension (I made the method that updated the inventoryitem object bold):

public class shipOrder_v0_3 {
public Sales_Order__c order {get; set;}
public List<SalesOrderLineItem__c> soliList {get; set;}
List<SalesOrderLineItem__c> soliIdList {get; set;}
public SalesOrderLineItem__c soli {get; set;}
public String shipQty {get; set;}
Map<String,Decimal> shipQtyMap {get; set;}
Map<String,Decimal> boQtyMap {get; set;}
public List<String> inventoryList {get; set;}
public Map<String, List<wInventoryItem>> availableInventoryMap;
public Map<String, List<wInventoryItem>> selectedInventoryMap {get; set;}
public String shipDate {get; set;}
public String trackingNumber {get; set;}
//public List<wLineItem> itemList {get; set;}
public Shipment__c shipment {get; set;}
public String currentLineItem {get; set;}
public List<wInventoryItem> currentLineItemList {get; set;}
public List<Map<String, List<wInventoryItem>>> selectedMapList {get; set;}
ApexPages.StandardSetController setCon;

    public shipOrder_v0_3(ApexPages.StandardSetController controller2) {
      String orderId = ApexPages.currentPage().getParameters().get('id');
      System.debug(orderId);
      order = [SELECT Id, Name, Shipping_Method__c,Collect_Account__c, Status__c, Ship_Collect__c,Ship_To__c, (SELECT Id, Name, Quantity__c, Quantity_Shipped__c FROM Sales_Order_Line_Items__r)
               FROM Sales_Order__c WHERE ID = :orderId LIMIT 1];
       soliIdList = (List<SalesOrderLineItem__c>)controller2.getSelected();
      Set<Id> idList = new Set<Id>{};
      //this is a test variable to try and get the VF page to display map data as desired
      selectedMapList = new List<Map<String, List<wInventoryItem>>>{};
      String idset;
      //setCon = controller2;
      System.debug('The number of selected records: ' +controller2.getSelected().size());
      soliList = new List<SalesOrderLineItem__c>{};
      System.debug(soliIdList);
      //define the details of the shipment object that will be inserted into the database
      shipment = new Shipment__c(Sales_Order__c = order.Id, Address__c = order.Ship_To__c,Collect_Account__c = order.Collect_Account__c, Shipping_Method__c = order.Shipping_Method__c);
      soli = new SalesOrderLineItem__c();
     
      shipQtyMap = new Map<String, Decimal>{};
      boQtyMap = new Map<String, Decimal>{};
      for(SalesOrderLineItem__c asoli:soliIdList){
        idList.add(asoli.Id);
        idset += asoli.Id +',';
        System.debug('The idList:' + idList);
      }
      System.debug(idset);
      //***********this if statement is to assist development. it should be deleted when development is finished*********************
      /*if(soliList.isEmpty()){
       System.debug('soliList was empty');
       idset='a03Q0000002Tvun';
       idList.add('a03Q0000002Tvun');
       idList.add('a03Q0000002Tvum');
      }  //*********** end this if statement is to assist development. it should be deleted when development is finished*********************
      */
      //itemList = new List<wLineItem>{};
      for(SalesOrderLineItem__c soli:createSoliQuery(idList)){
        shipQtyMap.put(soli.Name,0);
        boQtyMap.put(soli.Name, soli.Quantity_BO__c);
       // wLineItem lineItem = new wLineItem(soli);
       // itemList.add(lineItem);
        soliList.add(soli);
      }
      this.setInventory(soliList);
      System.debug('************** SOLIList: ' + soliList + 'availableInventoryMap: ' + availableInventoryMap + 'ShipQTYMap: ' + shipQtyMap);
      System.debug('************** boQTYMap: ' + boQtyMap);
      //System.debug('***************** lineItem list: ' + itemList);
    } // end constructor

    //***************Code for Adding/Removing line items to/from the selected inventory map *****************************************
 
  // displays the selected items
  public PageReference addToTempSelected() {
    String selectKey = ApexPages.currentPage().getParameters().get('selectKey');
    // if selectedInventoryMap is null, create a new map and add a null list for each sales order line item selected for shipment
    //System.debug('The current selected line item = ' + currentLineItem + 'CurrentLineitemList: ' + currentLineItemList);
    if(selectedInventoryMap == null){
      //System.debug('selectedInventoryMap is null!');
      selectedInventoryMap = new Map<String, List<wInventoryItem>>{};
      for(SalesOrderLineItem__c soli:soliList){
        selectedInventoryMap.put(soli.Name,new List<wInventoryItem>{});
      }//end for loop
      selectedMapList.add(selectedInventoryMap);
    }//end if
   
    // Instantiate a new temporary list to add user slected inventory to
    List<wInventoryItem> tempSelectedList = new List<wInventoryItem> {};
    tempSelectedList = selectedInventoryMap.get(currentLineItem);

    List<wInventoryItem> tempList = availableInventoryMap.get(currentLineItem) ;
    Decimal selectedQty = tempSelectedList.size();
    System.debug('Value of shipQtyMap for ' + currentLineItem + ' = ' + shipQtyMap.get(currentLineItem));
    //System.debug('tempSelectedList size before add: ' + tempSelectedList.size());
    for(Integer i =0;i< tempList.size();i++) {
      if(tempList[i].item.SerialNumber__c == selectKey) {
        try{
        selectedQty += 1;
        System.debug('added to tempList: '+ tempList[i]+ 'selectedQty: ' +selectedQty);
        if(selectedQty > boQtyMap.get(currentLineItem)){
          system.debug('**************** You have tried to add too much inventory *************');
          throw new InvalidShipQtyException('Sufficient inventory has already been added to this line item to fulfill the order - unable to attach additional inventory');
        }
        tempSelectedList.add(tempList[i]);
        }catch(InvalidShipQtyException isqe){
          tempList[i].selected = false;
          selectedQty -= 1;
          ApexPages.addMessages(isqe);
        }   
        }//end if 
    }// end for loop
    shipQtyMap.put(currentLineItem, selectedQty);
    System.debug('tempSelectedList after add: ' + tempSelectedList.size() + 'ShipQtyMap value for '+ currentLineItem +' : ' + shipQtyMap.get(currentLineItem));
   
    selectedInventoryMap.put(currentLineItem, tempSelectedList);
    System.debug(selectedInventoryMap.get(currentLineItem));
    return null;
  } // end method addToTempSelected
 
  // This method cycles through the list of selected inventory items and removes those that have
  // been un-selected by the user
  public Pagereference removeSelection(){
    System.debug('removeIndex: '+ ApexPages.currentPage().getParameters().get('removeIndex'));
    String index = ApexPages.currentPage().getParameters().get('removeIndex');
    String key = ApexPages.currentPage().getParameters().get('removeKey');
    System.debug('removekey: ' + key);
    List<wInventoryItem> tempSelectedList = selectedInventoryMap.get(key);
    List<wInventoryItem> tempList = availableInventoryMap.get(key);
    System.debug('Map: ' + selectedInventoryMap + ' List: ' + tempSelectedList);
    for(Integer i = 0;i<tempSelectedList.size();i++){
      System.debug('Iteration number: ' + i);
      if(index == tempSelectedList[i].item.SerialNumber__c){
        tempSelectedList[i].selected = false;
        tempSelectedList.remove(i);
        for(wInventoryItem wItem:tempList){
          if(index == tempList[i].item.SerialNumber__c){
            tempList[i].selected = false;
            break;  
          } // end if to change selected status in results area
        }  // end for loop to update selected status
      } // end if
    }// end for loop
    //selectedmap.remove(index);
    return null; 
    } //end method removeSelection
   
    //***************END Selected products add/remove code******************************************
   
   
    public PageReference selectInventory(){
      currentLineitem = ApexPages.currentPage().getParameters().get('lineItem');
      System.debug('selectInventory called! ' + currentLineItem + 'From Param: ' + ApexPages.currentPage().getParameters().get('lineItem'));
      currentLineitemList = availableInventoryMap.get(currentLineItem);
      System.debug(currentLineItemList);
      return null;
    }
   
    public PageReference doShip(){
      System.debug('Do ship called');
     
      try{
        Database.SaveResult sr = Database.Insert(shipment);
        //if the shipment object is inserted successfully attach specified inventory items and update Sales Order, Sales Order Line Item,
        //and inventory items with shipment ID
        if(sr.isSuccess()){
          System.debug('*****************************From doShip: Shipment ID= ' + sr.getId());
      
          for(SalesOrderLineItem__c soli:soliList){
            System.debug('SOLI: ' + soli + ' : key in map?: '+ selectedInventoryMap.containsKey(soli.Name));
            if(selectedInventoryMap.containsKey(soli.Name)){
              List<InventoryItem__c> itemList = new List<InventoryItem__c>{};
              List<wInventoryItem> tempItemList = selectedInventoryMap.get(soli.Name);
              System.debug('Selected QTY for' + soli.Name + ' = ' + tempItemList.size());
              //shipQtyMap.put(soli.Name,tempItemList.size());
              soli.Shipped_Date__c = shipment.Shipment_Date__c;
              soli.Quantity_Shipped__c += shipQtyMap.get(soli.Name);

              System.debug('shipQtymap value for ' + soli.Name +': ' + shipQtyMap.get(soli.Name) + 'soli qty value: '+ soli.Quantity_Shipped__c);
              for(wInventoryItem item:tempItemList){
                item.item.Shipment__c = shipment.Id;
                item.item.Date_Shipped__c = shipment.Shipment_Date__c;
                item.item.Sales_Order_Product__c = soli.Id;
                item.item.Status__c = 'sold';
                itemList.add(item.item);
                System.debug(item);
              }//end nested for loop
             
              update itemList;

            }// end if
          }// end for loop
          update soliList;
          updateOrderStatus();
          System.debug('Page should redirect 1');
          PageReference detail = new ApexPages.StandardController(order).view();
          detail.setRedirect(true);
          System.debug('Page should redirect 2');
          return detail;
          }// end if
      }catch(Exception e){
         ApexPages.addMessages(e);
      }
     
      
      return null;
   
    }// end method doShip
   
    public Map<String, List<wInventoryItem>> getavailableInventoryMap(){
      return availableInventoryMap;
   
    }//end getavailableInventoryMap
  
    public void setInventory(List<SalesOrderLineItem__c> soliList){
      if(availableInventoryMap == null)
        availableInventoryMap = new Map<String, List<wInventoryItem>>{};
      for(SalesOrderLineItem__c soli:soliList){
        System.debug('From setinventory: ' + soli);
        List<InventoryItem__c> anItemList = [SELECT Product__c, Name, Activation_Code__c, Sales_Order_Product__c, Shipment__c, Status__c, SerialNumber__c, Product__r.ProductCode, ProductCode__c
                                             From InventoryItem__c WHERE Product__c = :soli.product__r.id AND Status__c = 'inventory' ORDER BY SerialNumber__c];
        System.debug('from setinventory: ' + anItemList[0].ProductCode__c);
        List<wInventoryItem> wItemList = new List<wInventoryItem>{};
        for(InventoryItem__c item:anItemList){
          wItemList.add(new wInventoryItem(item));
        }// end nested for loop;
       
        availableInventoryMap.put(soli.Name, wItemList);
      }//end for loop
    }//end method setInventory
   
  
    //This method checks all the line items of the order to determine if the entire order is shipped
    //if the order is shipped the status is updated to 6-Shipped
    private void updateOrderStatus(){
      boolean allShipped = true;
      System.debug('updateOrderStatusCalled - Order Id : ' + order.Id + 'Status: ' + order.Status__c);
      try{
        for(SalesOrderLineItem__c soli:order.Sales_Order_Line_Items__r){
          System.debug(soli.Name +' Shipped QTY: ' + soli.Quantity_Shipped__c +'!! Order QTY: '+ soli.Quantity__c);
          //if(shipQtyMap.get(soli.Id) != null && Integer.valueOf(shipQtyMap.get(soli.Id)) > 0 ){
           if(shipQtyMap.get(soli.Name) != null && shipQtyMap.get(soli.Name) > 0 ){
             System.debug('This line item is being shipped in this shipment: '+ soli.name);
             if(soli.Quantity_Shipped__c + shipQtyMap.get(soli.Name)  != soli.Quantity__c){
               allShipped =false;
               order.Status__c = '5.5 - Partial Shipment';
               System.debug('allShipped? ' + allShipped);
               break;
               } // end if
             }else if(soli.Quantity_Shipped__c != soli.Quantity__c){
               System.debug( 'Soli shipped QTY: ' + soli.Quantity_Shipped__c + ' Soli qty: ' + soli.Quantity__c);
               allShipped = false;
               break;
             }else{
               System.debug('All BO for this line item is fullfilled! - ' + soli.Name);
             }//end if-else
            
        }//end for loop
        if(allShipped){
          order.Status__c = '6 - Shipped';
         
        }//end if
        System.debug('The so details: ' + order);
        update order;
      }catch(DMLException e){
        ApexPages.addMessages(e);
      }// end try-catch
     
     
    }//end method updateOrderStatus

   
    //method to create discountSchedule dataBase query
   public List<SalesOrderLineItem__c> createSoliQuery(Set<Id> sList){
       System.debug(sList);
       List<Schema.FieldSetMember> shippingInformation= SObjectType.SalesOrderLineItem__c.FieldSets.Shipping_Information.getFields();
       String query = 'SELECT ';
        for(Schema.FieldSetMember f : shippingInformation) {
            query += f.getFieldPath() + ', ';
        }
        query += 'Id, Product__r.Id FROM SalesOrderLineItem__c WHERE Id IN :sList';
        System.debug(query);
        return Database.query(query);
    }
   
    public class InvalidShipQtyException extends Exception{
    } // end inner-class


   // ******************** Inner  Classes ********************************************************
    // This code is used to process the required workflow when a WebPort Connects product is purchased.
    private class WPCService{
     
      private ServiceContract createWPCServiceAgreement(String ActivationCode){
        ServiceContract s1 = new ServiceContract(name = ActivationCode); 
       
        return s1;
      }
    } // end class WPCService
    /*This is our wrapper/container class. A container class is a class, a data
    structure, or an abstract data type whose instances are collections of other
    objects. In this example a wrapper class contains  */
   
    public class wInventoryItem{

    public Boolean selected{ get; set; }
    public SalesOrderLineItem__c soli{ get; set;}
    //public Map<String, String> parameters {get; set;}
    public InventoryItem__c item {get; set;}
    //public List<String> serialNumbersList {get; set;}
    //public Boolean multiItem{ get; set;}

    public wInventoryItem(InventoryItem__c inventory){
        //soli = sLineItem;
        selected = false;
        item = inventory;
        //Parameters = new Map<String, String>{'shipQty' => '', 'startItem' => '', 'endItem' => ''};
       // multiItem = false;
        //System.debug(inventoryParameters);           
    } //end constructor
   
   } //end inner class wInventory
   
    /* public class wLineItem {

    public Boolean selected{ get; set; }
    public SalesOrderLineItem__c soli{ get; set;}
    public Map<String, String> parameters {get; set;}
    public List<InventoryItem__c> inventoryList {get; set;}
    public List<String> serialNumbersList {get; set;}
    public Boolean multiItem{ get; set;}

    public wLineItem(SalesOrderLineItem__c sLineItem){
        soli = sLineItem;
        inventoryList = new List<InventoryItem__c>{};
        Parameters = new Map<String, String>{'shipQty' => '', 'startItem' => '', 'endItem' => ''};
        multiItem = false;
        //System.debug(inventoryParameters);           
    }
   
   } //end inner class wProduct */

}