OP, I don't know if you're still reading. You sound genuinely confused about what you should be doing here. And to be honest, you sound conflicted about who you want to help - your DD or your DH, as if you can only choose one. I agree that some posters have suggested you be tougher, others that you step back and it does sound contradictory. That's because they are just techniques, really.
If you look at the broader picture, it's not so confusing. There are ways that healthy family relationships are supposed to work - and how tough or gentle you are isn't as important as getting that healthy dynamic right. All posters here are in agreement that the dynamic in your family is wrong. At the moment.
You don't have to be super mum, but if you are serious about parenting your DD for the remaining years of her childhood - and there are precious few - you need to get help. Not super-nanny help, but professional family counselling help. If you can all recognise some truths, agree on whose responsible for what, get some agenda for moving forward, it won't be a minefield. But it will be scary, because it will quite possibly mean your DH and you facing up to the problems within yourselves and between you as well.
Be prepared for a good family therapist to zero in pretty quickly on DH's mental problems/associated behavioural traits and be prepared to look honestly at how that is really affecting other members of the family. It won't be easy but if it helps, it will be worth it. Because you are really, really in crisis at the moment.
You say your DD is no ordinary teenager - perhaps she isn't. She could say the same thing about you as parents. This is no ordinary family problem and other ordinary parents are not going to be able to help you much. You know I have problems with your attitude but I hope for your daughter's sake you take the trouble to move on now. But don't go round in circles - I think you can see it's destroying your DD as well as your husband -if in fact it is what's destroying him.