With the reRender attribute in the commandbutton and the dummyId on the outputPanel, the params get the correct values but my second "div group" is not displayed when I click the button and it should.

I'm going to write my new simplified code below.

Visualforce code:
 

<!-- dummy panel id -->	
  <apex:outputPanel id="panel2">
  </apex:outputPanel>

  <!-- div citas paciente-->
  <div calss="modal-dialog" style="display:{!if(mostrarCitasPaciente,'block','none')};">
    <div class="tablemodal-container">
      <apex:form id="tabla">
        <apex:pageBlock >
          <apex:pageBlockTable value="{!lstCitas}" var="citas" styleClass="table table-hover">
            <apex:column value="{!citas.Name}"/>
            <apex:column value="{!citas.CloseDate}"/>
            <apex:column value="{!citas.Doctor__c}"/>
            <apex:column value="{!citas.Doctor__r.Especialidad__c}"/>
            <apex:column >
              <apex:commandButton value="Ver cita" action="{!mostrarCitaIndividualPaciente}" reRender="panel2">
                  <apex:param name="doctor" value="{!citas.Doctor__c}" assignTo="{!doctorCita}"/>
            	  <apex:param name="especialidad"  value="{!citas.Doctor__r.Especialidad__c}" assignTo="{!especialidadCita}"/>
                  <apex:param name="fecha" value="{!citas.CloseDate}" assignTo="{!fechaCita}"/>
              </apex:commandButton>
            </apex:column>
          </apex:pageBlockTable>
        </apex:pageBlock>
      </apex:form>
    </div>
  </div>

<!-- 2nd div group -->
<!--div cita individual paciente-->
  <div class="modal-dialog" style="display:{!if(mostrarCitaIndividualPaciente,'block','none')};" reRender="panel2">
    <div class="tablemodal-container">
      <table align="center">
        <tr>
          <td align="left"><apex:outputLabel value="Doctor"/></td>
          <td align="center"><apex:outputLabel value="Especialidad"/></td>
          <td align="right"><apex:outputLabel value="Fecha"/></td>
        </tr>
        <tr>
          <td>{!doctorCita}</td>
          <td>{!especialidadC}</td>
          <td>{!fechaC}</td>
        </tr>
      </table>  
    </div>
  </div>

Controller code:
 

public class controlador{
    
    //Vars
    public Boolean mostrarCitasPaciente{ get; set; }
    public Boolean mostrarCitaIndividualPaciente{ get; set; }
    public String doctorCita{ get; set; }
    public String especialidadCita{ get; set; }
    public Date fechaCita{ get; set; }
    public String doctorC{ get; set; }
    public String especialidadC{ get; set; }
    public Date fechaC{ get; set; }

       /*More vars ....*/

   //Constructor
   public controlador() {
        mostrarCitasPaciente = true;
        mostrarCitaIndividualPaciente = false;
    }
  
  //Methods

  public void mostrarCitaIndividualPaciente(){
        obtenerCitaIndiviudalPaciente();
        mostrarCitasPaciente=false;
        mostrarCitaIndividualPaciente=true;
    }

   public void obtenerCitaIndiviudalPaciente(){
        doctorC = this.doctorCita;
        especialidadC = this.especialidadCita;
        fechaC = this.fechaCita;

    }

  /*More methods ...*/

}

What I want to do is when I click the button, the second "div group" should be displayed with the values corresponding to the row on the table, because the vars should have the value of the params.
I can see in the console logs that the params has the correct values but for some reason the second div group is not displayed, and this is what I want to solve now.

Thanks in advance.​