My stepmom keeps fighting with my mom?

My Step mom is jealous of my mother in every aspect and its really bothering me. She keeps fighting my mom on everything. If my mom tells me not to do something, my stepmom will tell me to go ahead and do it. If my mom says I'm not allowed to go somewhere, my stepmom will go out of her way to try and get me there. My mom is gorgeous. My stepmom is pretty too but she constantly compares herself to my mom. She'll say stuff to my dad about him still loving my mom or how she can't compete with her. She fights with my mom and will say stuff to her about me and my brother to try to make my mom jealous, like we have some kind of super amazing relationship with her. She told my mom that I wanted to move in with her and my dad and there was nothing mom could do about it. She also told her that when we are at my dads house moms rules for us don't apply. She will also talk bad about my mom to me. My mother is the epitome of human kindness and love. She's a singer and a musician and is basically everything my stepmom isn't. And its really bothering me. I tried talking to her about it and so did my dad. She thinks her behavior is perfectly fine and see nothing wrong with it. Any advice would be appreciated.