The only experience I can draw on is from raising my own two daughters to adulthood. I can say this: the worst period of a young girl's life in terms of discipline is the middle school/junior high years, age 11 to 16 or so. If your stepdaughter is a problem now, at an easy age for girls, you are headed for disaster soon.
Discipline has to be equally from both parents or at least unilaterally from one without the interference from the other. The biggest mistake young parents make is to forget that a child, no matter what age, is still human and thus can be quite devious and smart in manipulating any situation to their advantage. A child wll always gravitate to the easier disciplinarian. Moreover, in your case, it is entirely possible that the whole strategy of the child is to get rid of you, perhaps to pave the way for what every child of divorced parents wants: for their "real" parents to reconcile. Conversely, unless mentally ill, the child soon figures out when the "hammer" has come down and their antics no longer work.
Parenting is the most difficult thing I have ever done. To be a parent means to put your needs second, to die, if necessary, for the sake of the child, even if the child is not what we hoped he or she might be. Being a parent doesn't just mean going to ball games or getting ice cream, but also (like the parents of the accused craigslist killer) visiting them in jail, or, like my grandmother, pushing them around in a wheelchair because her son was born with cerebral palsy. If you don't get this, you can't be a parent, not really. You can't be "kind of" a parent any more than you can be "sort of" an airline pilot or an "occasional" heart surgeon. A parent doesn't just have a mouth to feed, but has a life to mold, a future to craft, a heart to comfort. And being a step parent must be the hardest thing of all. Are you up to it?
Either you are this child's "father" now, or not. If you are not, you shouldn't be there. The girl doesn't need an adult housemate. If you are, then start acting like one. Not just by disciplining her. Do you play tea parties with her? Do you read her to sleep? Do you watch her favorite shows with her? Do you watch her ride her bike? Do you take her shopping? To most men, this is like poking ourselves in the eyes, but in my case, I bonded with my daughters in shopping malls as they spent hours looking at shoes. If you are willing to do this, they start to see you really are a dad. No one but a dad wastes an entire Saturday looking at backpacks and skirts. She will start to listen to you as a dad if she starts to see and feel you act like a dad. If you are not allowed to, by your wife, then the problem isn't the child, it is with her. If doing these things doesn't appeal to you, you got yourself into the wrong situation. Unfortunately for the child, if you bail out, what lesson does she learn? That's it's okay to bail out of situations if they get a little tough? How can a seven year old learn self-discipline if the thirty year olds in her life seem to have none? After all, she can't leave. She can only act like a brat.