This is sure complicated! If I’m reading your letter right, your mom did back you up about not going to your dad’s any more. So give her credit for that.
It’s likely your mom just wants peace in the house and is probably caught between you and your stepdad. You didn’t specify what goes on between you and him, so I don’t know how to advise you about that. I do know that it isn’t uncommon for a kid in your situation to have problems with a stepparent, especially if that stepparent is trying to discipline you in any way. If that’s the case, maybe you need to consider having a mature talk with him and your mom about household rules and how to get along better.
As far as your mom’s concerns about your female friends, it may be that she is worried about sex. Instead of talking about it directly, she’s trying to limit your time with girls. If that’s the case, then, again, the best way for you to try to change things would be to reassure her that you are able to be just friends with these girls and that you do know how to keep yourself and the girls safe sexually.
I wouldn’t characterize your situation as “having to be nice”. Instead, I hope you can think about it as an opportunity to show your mom and stepdad that you are maturing and can be trusted. That requires talking things out rather than just being mad.
I wish you well.