Baby momma drama!!!

Okay ladies I need to know if I’m on the wrong here. Let me start off with I have an eleven year old from a previous relationship and me and her dad are civil with each other and I’ve meet the girl he’s with because I want to know who’s around my daughter. Now I have a almost 3 month old and my boyfriend and he has a 5 year old from a previous relationship. He got full custody of her in November so she lives with us. I take her to school everyday help her with homework. I do all the mom things without being her mother. I don’t ever expect her to call me mom because I know she has one. Her mother is the worst. She’s in and out of jail and just isn’t consistent with her. I told my boyfriend that me and him need to be a team when it comes to our kids. He’ll tell me one thing and when her mother calls or text him to have the baby he changes his mind and it bothers me because it only when it’s convenient for her. It upsets me when he changes his mind because he tells me one thing and the moment she wants to change things he just does. Help me girls. I never had to deal with this with my daughters father.