@Chel14 if you're still here.
Firstly, remember that a significant proportion of people on Mumsnet are strange individuals who seem to genuinely love telling a poster who is struggling that whatever they do is wrong. They love putting the boot in; I've been here 20 years nearly now and seen this tendency grow. So look carefully at the tone of the posts - are they genuinely tough love, or is there a wish to hurt behind them?
Secondly, few people have walked your path. Some, but not many. So some people will try to give advice and it's genuinely well meant, but it's not applicable in your situation.
Okay, to your actual posts.
I think you need to stop and think very very carefully about this man in your life. He is not automatically a bad thing. You, yourself, in dealing with a child who is acting in such an impossibly difficult way need support and love and care. If he really is loving are caring, to break up with him would remove a support that actually can help you in your dealing with a young teen behaving in a very difficult way.
I think you need to consider carefully and rationally if he really is as good as he seems. Does he 'ring true'? Can he be manipulative; is he suggesting ways to make your life better, or do his suggestions somehow make things worse?
Do you have outside, honest friends/professionals who can give you external feedback whether he is a good thing or bad for you?
I think a reality check here is a good thing. If the feedback, external and from yourself, is that he is positive - keep him. If not, then break up.
With your daughter, my heart goes out to you. My autistic older son was hell, although in a different way. (my second is coming up to puberty and I'm honestly wondering how to survive it - not a joke). Not only do you have the extreme events of the last four years you have hormones and puberty and school problems in the mix.
I think you need more help than you're getting but where can it come from? This may be it.
You need, absolutely, to keep firm and consistent boundaries and to keep on being loving. Despite all the hell that will break loose when you try to enforce boundaries, it is essential to give her an underlying sense of security, and in fact something to rail and fight against, to allow her her very considerable distress.
If she has shut you and everyone else off at the moment I think you have to accept that for now. She can only come to you at her own time. Are there any adults at all she can talk to? Teacher, out of school person? Having just one (and it won't be you) can tip the balance.
Beyond that you must take care of yourself. She's going through hell, but your own mental stability is vital and dealing with a beloved child going through this takes one hell of a toll on you. Do everything you can to keep yourself going, and yes imo if your partner is a genuine good one, that means his hugs and support too. It can make a world of difference.
One thing the posters suggesting you break up don't seem to take into account is that having a (genuinely constructive) partner is something that actually, will keep YOU going. Because you have your own mental distress and then you have to deal with this. You can't give if you're running on empty and if you end up destabilized and back in hospital it would be catastrophic.
As far as you possibly can, stay calm. Breath calmly through your nose. ~Try~ not to react strongly - the more you react the more the situation can spiral. Harder to do than to say! Keep in mind, always, that you are the adult and she the child and you can control your behaviour better than she can. Don't get drawn into shouting matches.
Keep suggesting things to do once or twice a week. Not all the time, that would be overwhelming. Keep talking about homework - she will reject it, but underneath she will know that you are still concerned and caring.
If you can endure these years then she may well come out the other side. There's going to have been damage, as you know. But there may be enough stability for her for her to come through and build, if you can keep a loving base solid enough.
It may be that in 4 years you will reconnect (a long four years). It may be that the damage has been too big and it takes longer. Possibly a long time. But if you can stay strong then the chances of her coming through are higher.
Right now school results matter a bit, but providing a solid base matter more. You're doing the right thing by praising her for a good day, though it might help to say 'that was a good day' and not say 'lets make it two'. Count each good moment for its own worth at the moment.
Small but pragmatic note - eat healthy, don't drink much alcohol, and if you can try to stay fit and try to sleep okay. Hard to do again, specially the sleep!
From my heart I wish you the best with her.