The OP is describing a child who is clearly very distressed and maladjusted
OK, so when you met her and held that therapy session... did you ask DD if she was just acting up, testing her strength, pushing hard at some boundaries... you know, growing up the gnarly way?
Because that is the first thing you do, when applying basic psychology. Never assume, never make a diagnosis, never suspect a cause/effect. Always ask, always ask twice, always check back.
Leaping to MH issues is an absolute no-no.
Maladjusted? Certainly. MH issues because of that? Not necessarily. OP and her DD may just be going through the power struggle many teens experience and, being a single mum, is feeling the full force of her teen's angst.
OP you say she is troubled at school but lovely with her BFs family. SO she is capable of being socially acceptable. You haven't failed her. Keep trying, talk to school, try to get her to talk to the school counsellor (most have them these days). If/when she is calm enough talk to her about responsibility going independence and that biting the hand that feeds her is a poor choice. Maybe suggest she gets a weekend job to pay for the phone contract.
In other words discuss with her the realities of growing up, being self sufficient and agreeing with her that she is old enough now to be more responsible for herself... and here are the realities.
She might respond well. If not, you can only keep trying and keep talking to school and trying to support her.
Good luck.