JMHO but at that age the more you flat out "forbid" something the more she will rebel against what you are forbidding... it is like waving a red flag to a bull... all reason goes out the window .
Get her in a program well away from the mother (and where she will find it difficult to leave) if...
as far as lies > kids (teens) can go really far with their their OWN parents (my 13 year old stood her ground about not taking my makeup even after I promptly went to her room, got her purse and opened it and she had the proof of her lie under her nose!)
I am in holland but I see enough on...