Girlfriends mother planning on living with us forever!! What to do?

I side with you. Your gf needs to make her choice...relationship or mom. The rest is up to her. Just be aware, she really might choose her mom, and think hard before giving an ultimatum..no one likes these but it sounds like you have done all you can do. Maybe you might need a person who appreciates you and wants to build a life together without the hassle of an in law involved.