I think what you mean is, how do I make a trigger fire when the player enters it the second time, but not fire when he enters it the first time?
If that's correct, then it's easy. If it's not, then please explain some more.
Make your trigger:-
Condition: this and done1
done1 is a variable which is set to true when the player completes the objective, which is some distance away from the trigger area.
At the objective you will have a trigger which will include:
On Activation: "1" ObjStatus "done"; done1=true
Now when the player goes back to the start/stop trigger the variable is true so the trigger will fire when he enters it.