Since the Vatican is a SOVEREIGN NATION, @POTUS can deal with it like any other state. Sanctions, war, etc.

What if he were to designate it a TERRORIST state?

As I understand things, cardinals are diplomatically immune because they're from the Vatican as a state. While you may not be able to arrest them, you can expel them. I think Lionel was talking about this. I will return with sauce. If someone else already has sause, please add. I've had 2 hours sleep in the last 24