Our kids' rooms are dog-free zones. It's just easier that way, and I suppose it does have the added benefit of making dog poop on their beds very unlikely. I'd do my best to keep cats out of there, too, if I was ever duped into allowing one into our family.
Cats are just jerks. It's such a shame, they start out so cute! I honestly think you may have a keeper, though, a cat with better assholery skills would have peed.