Feeling desperate and struggling to find help is a horrible feeling for everyone involved. My husband was in a similar position, watching me fall apart. He said he felt powerless and frightened.
Although I know it will be hard to hear, I have to say first that recommendations aren't allowed here (this is an anonymous forum and it wouldn't be safe to allow that).
But I wanted to post anyway. To simply say one thing... please stubbornly keep trying. Your daughter is fortunate to have you willing to fight for her.
If you get to a point where you feel your daughter is at risk it it time to go to the emergency room. In an emergency situation she will see a psychiatrist. It isn't ideal but the option is there.
What we did was ask everyone we knew. I had a referral to a psychiatrist and the wait was 6 months. Hubby knew I couldn't get through that. So he asked absolutely everyone. Friends, colleages, managers, family, local GPs, local hospitals, chemists etc.
Then he called every one he found until he found a cancellation. I had to go back to the GP that day and get a new referral. It saved my life.
If you phone ask to be put on the cancellation list. You'll get little notice but anything is worth a try.
I hope you find support for your daughter soon.
It is also worth considering counselling for yourselves once you are satisfied your daughter is safe. Caring for others can be exhausting and distressing.