what should i do?
let her come. you will regret it if you dont. We have to move on, IMO, this is part of the deal
Sometimes it’s just better to take the high road. This isn’t your birthday party, it is your child’s. If you make a big deal out of it, you are just giving your ex power over you. Like it or not, you are not together anymore, and he is going to move on. Set a good example for your kids. Be civil. Remember you are only hurting the kids by making a fuss out of it.
Maybe the strategy from now on needs to be that celebrations aren’t inter-mingled. Kids have two celebrations - one with dad, the other with mom. It doesn’t have to be a big party each time - maybe it’s just dinner with dad, or a special outing with mom (with presents, of course.) But the forced togetherness shouldn’t be required, in my opinion.