As in all things, you need to pick your battles. You could probably request that she not be present, but if your ex wants her there, then he can have her there. So this is not a good battle for you to pick. Consider that if this girlfriend lives with your ex, and your children spend time in the home of your ex, they will also be spending time with this girlfriend. It might be better for YOU and a more effective way of handling matters involving the kids, to enlist her support by welcoming her into the discussion instead of throwing a fit. She may be more willing to go along with your wishes if you don't try to pretend she has no part in any of this. Also, consider the effect on the kids to have bickering between the two households. They don't need to hear you adults badmouthing each other. They have to live and get along with all three of you. Trying to exclude the girlfriend is only going to put your ex on the defensive. Sorry if this isn't the answer you want to hear. It is the reality of the situation and you need to make some sort of peace with that for the sake of your kids.