Hooray, someone who knows the correct spelling of separated! Now we just need to work on losing! (English majors have to get their kicks somehow.)

Do what you are comfortable with. He moved out of the house. Seems reasonable to me to say that no, you are not comfortable with him having a party for the kids when you are not there. The actual day of a birthday party is not as important as when people who are important to the birthday celebrant are available. The party should be at a time and place where you, as her mother, can be present. You are not divorced yet. Don't take a backseat to being part of your kids life, no matter whose "weekend" it is. And remember, he abused you on mother's day. He needs to show you he can be nice now.