Your first problem is: she is 13..... do I need to explain further?
At this age my daughter decided that living with her father would be so much better.....and she started telling different stories at each household. This was a 40,000 dollar mistake on her part. After fighting the court for a year, I told her to go live with her dad, then less than six months later, she was begging to come back, and is back for over a year now. The mistake here was not communicating with the ex .... and letting the kids rule the show.
I let them walk all over me, because I didn't want them to think I was the bad parent. I put a stop to that, and things are better.....but it's about as slow a process as grass growing. The kids still fight.....and what I noticed was, we could be anywhere, a restaurant, grandma's, movies, and they would be the greatest kids, and the very SECOND we stepped in our own home, they acted like monsters.
They did therapy for a year, separately. Can't say it did much good. Probably made them dwell on their problems more, instead of helping.
The only real effective punishment I ever gave, was the day they were fighting non-stop, I made them sit together on the couch, and hold hands. They screamed like I was beating them. They cried. They squeezed the others hand. They promised to be good. Each time, I restarted the timer, like a timeout for little kids. Eventually, they sat quietly for the full amount of time and still talk about that to this day.
Meanwhile, AH and I were in kitchen laughing our azzes off....and trying not to let them hear. They were about 8 and 10 at the time .....
Anyways, divorce is pretty tough on them, and I think that's about when my kids started acting out, but don't let it continue too long, or you will regret that.