Punishment is not the answer to this problem. It may buy you time on occasions but could result in a lifetime of hate from a child who will grow into a woman who remembers a harsh stepmother.
My clear impression is that your stepdaughter has unresolved emotional issues connected with the separation of her parents and, perhaps, what she sees as your part in it. You don't need to post personal details about that on this public forum and the facts as you see them aren't the most important version of events anyway. Your stepdaughter's perception of what happened to her family and who is to blame is all that matters in connection with the problems that you describe. What is certain is that she was an innocent party in the separation. She is still a child but a hurt one that is growing into a teenager with all of the issues that accompany that process for any child.
Counselling, effective though it can be, works only for those who are ready for it. Clearly, your stepdaughter is not. What might me more fruitful would be for you and your husband to seek professional advice about the problems of families such as yours. If the two of you can get proper guidance on how to control her whilst behaving towards her in a way that will gradually help her to come to terms with her family's issued you will be doing a good job. Control and punishment without understanding, love and support will not help her deal properly with her issues and you will have problems for a long time. There is no quick fix for a hurt child.
Your husband cannot deal with this alone. He has divided loyalties, pain and, perhaps, regrets to deal with. You have your own emotions to deal with too. No single one of you is more important than another. If you and your husband get the right help you may get through this as a family still intact and his daughter will accept, finally, life as it is. If you carry on as you are in that family group you will all continue to be unhappy and an innocent child will turn into a very damaged adult.
Good luck to each of you.
A little history may help perspective, she was living with her mom and who she was told was her dad, and her brothers and sisters. In this house the "dad" was mom's boyfriend and he was abusive to her younger brother who was not any blood of the "dad" but his sisters full brother, even though they were told that this brother had a different dad who was a bad guy (who was really their real bio father DNA test done etc.) The youngest child was the bio child of the mom and the boyfriend, not my husband's child. The eldest who is this girl was treated very well compared to the other kids besides the youngest "dad's" bio son. The reason for this was because she was the one playing mommy, taking care of all the kids while her bio mom was under the influence. Even though (what she thought was her half brother) was being beaten and starved she was comfortable being able to hit the other kids when they were bad.
I met my husband when he had just came out of prison for 2 years. The 2 years he was unfortunately gone from his children's lives, the mom had changed their names, all cept the boy, and moved them to a different town. DH had no idea where his kids were and had no help finding them cept me. He found out they were in the system two years later and we were making trips out of state once a month to go visit his kids. All made possible with my money I had gotten from an inheritance. Not only that, the people in charge weren't going to give this man his kids with his background and single. He was lucky he had me and our daughter to ease their minds. Don't get me wrong, the kids are where they are supposed to be. DH loves his kids very much. He is a good provider, but our marrige has gone to poop. I have given so much for him to be happy. So many people warned me not to take in his kids. My mom, my aunt, my grandma, even his boss. I am such an idiot.
They have no contact with their bio mom, who this girl says she hates. So she can't have the notion that her dad and bio mom are going to ever get back together. Actually, she had no idea that DH was her father until we met them.
You voluntarily joined a family that, from what you now write, is very dysfunctional. You might want to think about why you did that. I wonder whether your husband's motives regarding you were partly to do with getting more access to his children. I don't know but I wonder.
Set aside any advice to merely cut and run and just reflect for a while longer. You are saying more clearly now that your marriage is in trouble and saying it in a way that suggests the cause is not just your stepdaughter. If, the girl apart, you want to continue with your marriage then you have to help deal with all of the problems. I have already suggested that you and your husband, if he is willing, get some advice. If the marriage is over, with or without his daughter on the scene, then you have to make some plans for yourself and your own child. As you seem to acknowledge, your child's emotional well-being and development may be at risk and that is probably more important to you than the well-being of your husband's child. I'm assuming that your husband is not the father of your child.
Your stepdaughter hasn't had a good start in life, has she? Calling her a sociopath might be going too far but she could be heading in that direction if adults around her don't change their ways. Even if you stick with, it you can't help her if no-one else is behaving appropriately. That leads me to something else that has crossed my mind. Her mother seems to have some issues of her own. Is she influencing her daughter against you and her father?
I have suggested things that you might consider to help the girl but you have now brought into the picture some additional influences that might make your efforts ineffective. When I worked with clients who sacrificed themselves for the benefit of to the point of misery and despair, I would sometimes point out that, ultimately, we are each of us alone in the universe and have to take care of ourselves first. Clients who then suggested it was good to help others would then hear me say that they would do a better job if they sorted out their own issues first.
Finally, for the moment, if you want to leave your present family make the decision yourself and don't seek the approval of others here or elsewhere. You have to take the responsibility alone.