Hmm...surely the best way to approach the problem would be to mimic the ways that the Papacy was challenged historically?
Appointing an anti-pope happened a couple of times and, inevitably, the anti-pope was immediately excommunicated by the legitimate pope (go figure...). The only legitimacy the anti-pope had was with whoever was the secular backing behind his appointment (generally the HRE) and unless the real Pope had been deposed, the anti-pope installed and the entire Catholic community didn't rise up in violent disgust, then nothing would have come of it.
Total number of anti-popes who became pope? Nil.
So, rather than over-complicating matters, perhaps a flavour event that could trigger for catholic Kings to renounce the Pope's legitimacy and appoint their own anti-pope. The randomly selected character (unfortunate he...) would then be excommunicated as, most likely, would the King. The advantage of taking this route would be to avoid an equally grim alternative offered by the Papacy, such as Umam Sanctum (the King accepts that the Pope is his rightful liege - enormous loss to prestige and gold, change to church-strength laws), resist the Papal Bull (enormous loss to piety, loss to gold) or renounce the Pope (appoint random anti-pope who is excommunicated, chance of King being excommunicated and, ideally, loss of prestige to Pope and Papal Controller).
This event would then play out with the excommunicated characters later having the chance to reconcile with the Papacy through the normal event channels. No need to declare that their populace are heretics - they haven't turned protestant, they're just being encouraged to believe that the Pope in Rome isn't the rightful catholic Pope.
Regarding puppet popes, it would be a nice flavour if when the Pope is forced out of Rome and steals someone's land...sorry, 'relocates the Papacy', then the liege at the top of that particular food chain should have a decent chance of being appointed Papal Controller, much like the Avignon Papacy. This would only be temporary - any new Pope wouldn't necessarily be so lacking in will (as they weren't).
