Run away, run away.
This will only get worse the older she gets. And if you do happen to marry and have children with him, he will display the same permissive behavior towards your children. Now all of a sudden you have a 15 year old, who doesn’t have any control, and is self destructing, while you have small children at home. I have seen it on many occasions, the step mom loves the husband’s child, until she has her own. She prioritizes her children, (rightfully so,) the father is enamored with his new family, the step daughter feels completely ignored (which it seems might be happening already) and acts out even worse. The step mom is overwhelmed with raising small children, and really doesn’t have the time nor the patience to deal with the step daughter and her issues. Bad for everyone involved. Disaster in the making. What happens if instead of pushing you, she pushes one of your kids?
Can you get beyond all that, and make a loving happy home with all involved? Sure, people do it every day, but it’s going to be really, really difficult, especially since it appears that neither parent is willing to help. Personally, I’d take a pass, life is hard enough.
Why are you willing to put up with this?