I've only ever had one cat, by coincidence supplied by flashy. (Nice cat shame it had your attitude).
However, I suspect that because you take your first cat into the bedroom then shut the door, the new cat is trying a dominance thing.
Either let it in the bedroom or shut both out, the new cat will learn it's place when your first one gets annoyed with it.
At least then you'll only have blood and guts to clean off the carpet.