Don't play with drunk people.
Seriously. If she's so blasted that she's being irrational and uncooperative, then--sorry, sister, thanks for playing, go sleep it off.
I have a very low tolerance for the inebriated, so I avoid hanging around them. Likewise, the OP might wish to define his/her tolerance for drunkenness at the table and say, in no uncertain terms, "Not past this". Being that drunk at the table is obviously disruptive, and it's clear that the OP doesn't enjoy such tipsy shenanigans. Ergo, don't play with drunk people, whatever "drunk people" means to you.