I hope you and DD are having a lovely Christmas OP. Just popped on to share my experience with you. I took an overdose at 13. I had one counselling session while still in hospital and then a few family sessions afterwards. I can't say it made much difference to the family dynamics that I was desperately unhappy about.
I had art therapy but that wasn't really helpful in itself either. But one phrase this therapist said really stuck with me. If I'm not happy with something, change it.
I've had a very challenging life since then, with many tough situations that have left me feeling very low. I've never once thought about hurting myself again. I've never felt the need for anti depressants. I've always felt in control - if I don't like something, I need to change it.
I was homeless at 16, but still went to University. I was in an abusive relationship at 18, but left the same day I realised he had crossed the line. I met the man of my dreams but then struggled to conceive. 5 years and 2 rounds of IVF, we had our precious miracle, but having a child left my physically disabled. I still went back to work full time after 12 months and continued my career. I'm mentally strong and resilient.
If I'm not happy - it's up to me to change it.
I didn't have any formal CBT but that is the underlying message, it's practical and teaches you the skills of how to change your thinking about situations as well as solving problems in a practical way. The more practice she has at solving problems and overcoming difficulties, the more she will feel able to deal with them. I've been made redundant 5 times and now wouldn't bat an eyelid if when it happens again, just dust off my CV and use my exit package for an amazing holiday!!
Good luck OP and much love to your DD 