I have a Parent object (Contact) and a Child object (Customer__c). The Child object's text field (Corp__c) values in order of weight are: "Very Viable",  "Averagely Viable", "Somewhat Viable", "Not Viable" and "Indifferent". If a parent record has two Child records so that Corp__c for the two records are "Averagely Viable" and "Not Viable", then I want a picklist field on the parent to update as "Averagely Viable" (since "Averagely Viable" has more weight than "Not Viable").
My first question is :
Can I write a trigger on a managed package (The Custom Object Definition is managed)?

Secondly, I've written a trigger for newly created Customer records for a start but it is just not working. 

trigger CorpUpdate on Customer__c (after insert) {
    if(Trigger.isInsert){
                          try {
                     
                    for (Customer__c co : Trigger.new){
                        Contact po = [SELECT Id, picklist__c FROM Contact WHERE Id = :co.npe5__Contact__c];               
                      List<Customer__c> l_co = [SELECT Id,Corp__c ,npe5__Contact__c FROM Customer__c
                       WHERE npe5__Contact__c = :po.Id];
                        for(Customer__c am_co : l_co) {
                            if(am_co.Corp__c  == 'Very Viable' || am_co.Corp__c  == 'Averagely Viable') {
 
                            am_co.Corp__c   = 'Very Viable';
                        }
     
                        else if (am_co.Corp__c  == 'Very Viable' || am_co.Corp__c  == 'Somewhat Viable') {
                         am_co.Corp__c   = 'Very Viable';      
                       }
                      else if(am_co.Corp__c  == 'Very Viable' || am_co.Corp__c == 'Not Viable' )
                        {
                        am_co.Corp__c   = 'Very Viable';
                        }       
                    else if(am_co.Corp__c  == 'Very Viable' || am_co.Corp__c  == 'Indifferent' )
                     {
                        am_co.Corp__c   = 'Very Viable';
                    }
                    else if(am_co.Corp__c  == 'Averagely Viable' || am_co.Corp__c  == 'Somewhat Viable' )
                    {
                        am_co.Corp__c   = 'Averagely Viable';
                    }
                    else if(am_co.Corp__c  == 'Averagely Viable' || am_co.Corp__c  == 'Not Viable' )
                    {
                        am_co.Corp__c   = 'Averagely Viable';
                    }
                    else if(am_co.Corp__c  == 'Averagely Viable' || am_co.Corp__c  == 'Indifferent' )
                    {
                        am_co.Corp__c   = 'Averagely Viable';
                    }
                    else if(am_co.Corp__c  == 'Somewhat Viable' || am_co.Corp__c  == 'Not Viable' )
                    {
                    am_co.Corp__c   = 'Somewhat Viable';
                    }
                    else if(am_co.Corp__c  == 'Somewhat Viable' || am_co.Corp__c  == 'Indifferent' )
                    {
                    am_co.Corp__c   = 'Somewhat Viable';
                     }
                    else if(am_co.Corp__c  == 'Not Viable' || am_co.Corp__c  == 'Indifferent' )
                    {
                     am_co.Corp__c   = 'Not Viable';
                    }
                    else {
                  am_co.Corp__c = 'Indifferent' ;
                  }
                 po.picklist__c = l_co.Corp__c;
           }             
           update po;         
      }
      
            } catch (Exception e) {
                System.debug(e);
            }
        }
   
  
}


     

I'm a newbie when it comes to Triggers any help would be greatly appreciated!