R.M.
You didn't tell us how old this child is? At least an adolescent, if not a teenager. I can tell you, from personal experience that stepchildren who have been raised in a different way that you are used to can be a huge source of stress and disagreement in a marriage. BUT I think you are making a huge leap to be talking about leaving your marriage!!
You and your husband need to find a 3rd party ( pastor, counselor etc) to sit down and talk over all of the issues surrounding this. But you need to be willing to view your stepdaughter as a confused child who is possibly acting out to try and make her parents sit up and take notice of her. Think of how you would handle this if it were YOUR daughter doing these things. You can't just demand that she live according to your standards...you need to start by building a relationship with her...as a friend and mentor...find teachable moments to help her learn the right way of doing things.
As I said before...it is hard to really give you good solid advice without know what age your stepdaughter is.
Please don't give up....my own stepson who is now in his late 40's was SUCH a handfull as a child...he lived with us for a total of about 7 years and I am not ashamed to tell you that I felt like throwing a PARTY when he left for the last time...and was joining the military so I KNEW he wouldnt be moving back in again!!! But...fast forward to 2011...although his home is not exactly what we would like for him to have as far as the way he is raising his children and grandson...we have formed a real friendship...we enjoy each other...and he feels much closer to me than he does to his biological Mother.
Good luck...you will need big stores of patience and love and concern.