I agree with Kira Stepfathers can be very difficult
I gained a stepfather only at 2 years old (I moved in with them at 7)
I still "hated" him in my teen years/ he never ever disciplined me ever.. I just disliked this blue eyed blonde man who I felt like I would never fit with.
as a youth I thought he was cold hearted and mean
as an adult I have come to the understanding we have way more in common then I ever thought more so then my real father that I felt like I was protecting my whole life (yes he is my father and I care for him but he is a real loser)
I don't know what is going on in your house hold but if they are fighting like siblings it sounds like he is engaging in the situation
she is a pre-teen girl... in the best situation she would still be hell on wheels. He prob needs to back off & just ignore her antics & just leave her be