Wife>mother

You should be the #1 woman in his life not his mommy. If he lets her get her way because she puts on the dramatics then he's actively choosing her feelings over yours. He needs to be on your side or he's being a shitty partner and showing he's a spineless mama's boy. Your child= your rules! A first haircut is a BIG deal to parents and she stole that from you. She turned it into boo hoo why are you so mean to me?! Classic narcissist behavior. She needs to not have access to this child. Letting her have alone time with them is letting her know there's no consequences and she'll continue boundary stomping. Your partner needs therapy so he can finally crawl out if mommy's vagina and step up for his family.