Cats can be trained! But not someone else's cat, yeah. Okay, a few things: cats don't like to be moved. I'm assuming, considering he's broken a vase, that he's been temporarily relocated from elsewhere? That's not helping matters, I'd guess. When I catsit, I do so with the cats remaining at their usual home.

Is there a reason that the litterbox needs to be accessible through RR's room? Because my immediate response to that situation would be to move the litterbox and let her close her door, too. Cats are pretty independent beasties, and, with you guys (and hopefully anything breakable) safely behind doors, he should be able to amuse himself.