You send your daughter to her grandparent, Right?
You told she will get back when she will learn to behave, right?
You also told that your mother undermine you and support her, correct?
Now will you please tell me, How is she going to learn to behave well, after living with the person supporting her?
Instead she won, because she no need to follow you rules anymore or tolerate or bear you any more in her language.
She got what she wanted and you lost by a 15 year old girl.

