I am so sorry you have to dael with this, unfortunly I think this happens alot as teens are hard at the best of time and when they have the option to leave they ALWAY throw this in your face....

My sister when to school with a girl who from yr 7 to yr 12 would spend 6 mths with her mum and 6 mths with her dad ( and she was an only child on BOTH sides so its not just because you have other children its just because she is a teen ) because she would keep telling them that she didnt want to live with them anymore but once she got to the other parents house she would last 6 mths until that parent did something she didnt like...

I think that you and you EX need to get together with some ground rules as she could play this out for a very long time, and as you said she is used to getting her own way so she will try very trick in the book...

If you are happy for her to live with Dad then let her but DONT let her play you both off each other... All teens go though not wanting to be with there parents its just not all teens have a get out of jail free card iykwim....

I hope it gets better soon