I can only imagine how tough this is. It's great that you got rid of the violent and controlling husband (which takes great strength) and that you are moving into a better situation as a single parent.
It sounds like your daughter is an a largely stable situation, getting good grades and saying she at least has a plan. She's showing some signs of being strong. Moving out of town with you would certainly disrupt that, and she's already had plenty of upheaval.
I hope that your parents are controlling the credit cards and shopping sprees, but if they are spoiling her a little, I think it's understandable. You don't say whether her father is in the picture, but if he's not and now she has also (from her perspective) seen you choose a man who didn't value you yet you didn't fight to keep her at your home, she may feel she's been abandoned by 2 parents (or at least placed her further down on their priority list). If they are making her feel special, that might be okay. I wouldn't say a thing about fake nails - that seems like really small potatoes even if you wouldn't have permitted it.
It's hard to know what you mean by "gone on weekends" and "out of town with people we don't really know." Who doesn't know the people? You? Or your parents? You haven't been in her life much for the past year so you probably aren't in a good position to pass judgment here. It's possible that your parents know them better than you do.
I'm a little concerned by her statement that you shouldn't leave your husband and the house. That suggests that she thinks a woman should put up with anything just to be married and have material things, so mixed with her desire to purchase material things, she may be headed down the wrong path. But I don't think there's anything you can do about that in the short run.
The first thing you should do is try to have a relationship with her, and that means giving up talk about her moving in with you. Living with your abusive husband and watching you choose him over her (in her view), along with the year in between, has changed her. It will take time to help her find herself (even though she thinks she has done so). You will need a lot of time for her to trust you, see the changes in you, and admire you again. So start with simple things that don't involve telling her what to do and not do, especially regarding her friends or superficial things like clothes and fake nails. Go out to dinner with her (get a sitter for the baby if you can), attend her school events, go to teacher conferences, and go to her annual physical. Just be in her life. You can talk, over time, about how you have changed and how you have found your strength and backbone, and how you have learned that a man cannot be the be-all and end-all for any woman.Just let her absorb that from your point of view. It will take time to show her you are strong, you aren't going back to the abuser, and you have changed your world view. Your goal is to be welcome in her life, to gradually meet her friends, and to slowly reestablish yourself as an admirable role model. You can ask your parents to modify a few things but you really have to be sure you have all of the information and also that you don't come across as bossy since you have made your own bad choices. You really have to be so grateful to them for giving her stability and love.
As you get back with her, consider the scene you describe of wrestling her phone out of her hands. That just doesn't sound like something a mature parent would do. She also called your parents AND they actually took her to their home - so your maternal authority was suspect or fragile from the get-go. You can't just muscle your way back into her life and "wrestle her away" from her life, friends and choices. Your influence must be much more subtle and supportive, and you have to prove your ducks are in a row. I don't know if she will ever live with you again, but I do know that trying to force it will drive her further away.