A very serious question about my 5 year old.?

My 5 year old has been misbehaving more often lately, by not listening, talking back, etc. My husband was raised alot differently then me and I do discipline but with love. And he is just constant discipline. He doesn't ever really spend any time with her. He is not biologically her father but her real father was very abusive towards me and when she was about 3 she witnessed him pushing me down a flight of stairs and constant yelling etc. and has nothing to do with her life. My husband says he wants to be her dad but all he really does is discipline, hardly takes her outside, hardly does any activities with her. I know he loves her. I have tried to address the situation to him and how it makes me feel but it just leads to an argument. I don't know what to do, I feel like my daughter is going to start hating him, and is starting to act out more cause shes thinking thats all the attention she is going to get. He thinks hes right about everything and it just ends up getting thrown out and it continues and I hate seeing my lil girl get into trouble constantly, it tears me apart......what do I do? Am i doing something wrong? HELP!!! Oh and to add we just had a baby as well, could that have something to do with any of this?