Catholic Diplomatic Immunity

Here's an idea. 

The Vatican is a state - a very small one, but none the less it is, in international law, a state. And states have diplomats.  And diplomats have a special legal immunity under the Vienna Convention on Diplomatic Relations (1961).

So how about the Vatican making all it's priests and prelates diplomats - envoys of the Vatican.  After all, that is pretty much what they are, the Pope's man in your parish.

And then all the priests who break vows of chastity, especially the ones who both break vows and break law, could really be above the law.  Better yet, the host country could save themselves all the difficulty and cost of arresting and trying a priest.  They could simply declare the Vatican diplomat to be persona non grata and get them shipped back to the Vatican.