Dealing with your fiancées newborn child and the mother

I’ve been talking to my fiancé for about a year now and while we were dating in the beginning he told me he had a child on the way. In the midsts of it all, he stopped talking to me and tried to get his “family back” and left me hanging in the dark. so after a couple months it didn’t work out because his baby’s mother already has a child and he says that’s the reason they can’t be together is because her daughter doesn’t listen to him and she won’t enforce rules or boundaries. The baby they have now was planned according to him thinking it would make their relationship better when it didn’t. Anyways, I really love him so we got back together shortly after and I forgave him. She found out he was talking/getting engaged to me and called him cussing him out saying she wasn’t gonna give his daughter his last name. This broke his heart and I’m the one that has to deal with his emotions. The baby was born at the end of June and she has been very annoying and rude. Threatening him with CS when he’s been doing nothing but say yes to her every need. She doesn’t even want me holding the baby and honestly my feelings are hurt.. he has to go to his fathers just to spend time with his daughter. Or he has to go to her house. He even started being sneaky about it cause he knows it hurts my feelings I haven’t done anything wrong but love and accept the child and honestly it’s turning into anger as time goes on. Any advice? I love the baby because she’s apart of him and haven’t even gotten the chance to meet her. How long do I let this continue?