Hi there Karen - welcome and thanks for being such a supportive mother!

I can try give you my insight - I'm 24 and no doubt give my mother grey hairs!

I moved out of home with a boyfriend when I was 19, and she was OK with that. (The bf and I am still together). My mother does not know I am presumably BP (We don't speak that much, but have always had a positive relationship; I just never discussed very personal things with her).
Last year Feb my world crumbled a bit, with me breaking up (temporarily) with my bf, my boss at the time took me under her wing and I moved in with her. I was first diagnosed with Major Depressive Episode and went to hospital for a few days. My boss phoned my mom; also informed her I had started smoking. (Note the shattered image this was to my mother, who had only known me a straight-A student, who was in a well-paid job, and getting towards the end of her career).
She came to see me in hospital and was very supportive. Even now she will send me the odd informative article she finds along the way.
She doesn't know about my BP and I guess it's easier that way. I do know that if I need someone to lean on, she's there.

Personally, I never had a problem admitting I suffered from depression; or now, with BP. I understand it's a medical condition, I understand medicine helps. I understand that the hospital is a measure that can be used too.
Is it possible for you to get your daughter into hospital? If she suffers from BP, the mania, if left untreated, can be dangerous.
I tried to take an OD when I was in my deepest darkest depression. I hurt my family badly. I realised only medication can take that pain away. I've avoided therapy, as I am battling to pin-point issues that I feel I need to work on, but they are slowly becoming clear to me.
I think you are practicing tough love, which is not easy, but may be necessary to cause the break-through in your daughters thinking. I truely hope she comes round soon enough and lets someone help her