Im going to stick up for your ex here as I think she was well within her rights not to allow your gf to your daughters party. I mean why the hell would she want to go anyway? To keep an eye on you? To piss off your ex? To upset your daughter?
People think that birthdays are just about kids and they are but mum's celebrate them as a very special day to. Birthdays bring back all the memories of the day they are born, the reflection and sadness at how much they have grown and the fears about their future. Your ex was pregnant, gave birth and is raising your daughter. If I was you I'd rather focus all my attention on my daughter on her special day and not worry about your ex and gf fighting - your daughters (3rd,4th,5th) birthday will never happen again! You and your ex are her parents and even though you arent together that doesn't change. Daddy bringing his new gf and upsetting mummy isn't going to pan out well for your daughter's memories so in my opinion - your ex was absolutely right and your girlfriend needs reminding that he is your girlfriend and not your daughters mother!
Good luck x
My Milkshake Brings All The Boys To The Yard
imagine having your ex wife and partner in the same bed, its odd and not normal but the sex would be so good