I don't want my brothers girlfriend around on Christmas Day
Why don't you want her there on such an important holiday?
Because she's a psychopath. She won't leave us alone
It's your right to choose who you invite to your family functions. However so does your brother and telling him that he can't have his girlfriend around will likely upset him and cause a fight.
Let the drama play out.
Why not just have a sincere talk with him before hand on why being around his girlfriend upsets you? He may be willing to listen to you and change his plans to go with her family instead. It's better than just making demands of someone and instantly upsetting them.