The French kings in practice held the Popes hostage somewhere in southern France (I can't recall the name of the place right now) for around a century or so. The power struggles between the Holy Roman Emperors and the Vatican saw several instances of at least two parallel Popes, one of them the Emperor's lackey. And so on.

Personally I don't think it'd be a good idea to try to put the more complicated Papacy-related politics into the game. I've some doubts of the system's ability to handle it in the first place, and what has thus far been told of related things seems to do the job passably well.