Me and my daughter's father were married and I could swear I was reading my marriage in your post. He would lie all the time and was very disrespectful and started being abusive. I grew so much resentment and realized that even if he did change to my perfect man ideal I STILL would not enjoy his company or love him the same way. Of course my daughter was young but even if she was older I still would've divorced him. If you talk openly with your children and explain what is going on and just be there to reassure whatever their feelings are about the whole thing, help them through it, then they should be fine. I think maybe your husbands child is that way because noone did that for her or maybe she was "conditioned" to be that way towards you or your husband (spiteful mother?).
It was sooo hard leaving especially when he would PROMISE he'd change, we went to marriage counseling and he lied to the counselor about things he was doing present-day behind my back (apparently). I left him before and took him back with promises... it's always good for two weeks then back to the same old fighting all the time, him lying about everything small to big, and me wondering why I took him back. You won't ruin your kids' lives, they need to see you happy! After I left my exhusband my daughter was actually happier because I was happier, my mood rubbed off on her. Like I said just talk to them throughout the process.
Please don't stay in an abusive or unhealthy marriage! I look back and am so happy I FINALLY made the decision because there were so many times I see now I should've left but didn't have the strength to leave because I thought for some reason I needed him or I wouldn't be loved by anyone but him even though he made me feel so ugly and worthless (apparently I'm gorgeous by what other people say lol), my self esteem was ruined for a whileee.
Good luck... sorry for the novel ;P