Tbh, at 12 she's old enough to decide that and probably will on more than one occasion, all you can do then is make sure she's aware of your desire to see her and leave her to come to you. The mother and her antics will become irrelevant the older the child gets, but try to stick with it and imagine if you were in her situation, you'd feel, angry, hurt, erratic, unable to properly communicate how or why you were feeling that and would likely lash out. That's all she's doing. With regard to the enormous dramatic lies, it's an attention seeking thing, when you find one out just calmly mention it and don't get into a slanging match about it, and just give her plenty of positive attention the rest of the time. It's a long haul job, but it'll be worth it.