You're amazing, no doubt about it. Everything you write amazes me. The fact that you just won't give up, despite being thoroughly exhausted and depressed is amazing. Ending a marriage even though there was possibly some feelings of low self esteem amazes me (such strength in times of challenge). Rebuilding a life without a partner is an undeniably amazing undertaking. Facing the heartbreak of seeing your kids face painful challenge after challenge but still managing to give them everything you can, under the circumstances, amazes me. I could go on but I think I've already established how stunning you are.
Being amazing can be thoroughly exhausting. How many times have you thought 'Gee, I wish someone else would do all this (amazing) stuff. I just don't have the energy anymore'? Under no circumstances should you doubt how well you are doing. On the other hand, I believe it could be a bit of a self esteem booster to perhaps doubt how well others around you are doing. I'm not out to start a blame game or anything, just want to try and shift perspective. For example, you take your daughter to professionals for mental well being purposes and she seems to be slipping further into a depression. Have you ever questioned these professionals? 'Why is my daughter doing worse than ever?' is perhaps a question worth asking the people who are meant to be serving her. 'What do you think you are doing wrong?' would be a seriously bold question to ask. Maybe asking your daughter whether she feels any great connection with her therapists could give you some answers.
I'm wondering where all the people are who could be raising you and your kids, to new possibilities, maybe some new outside the square strategies or therapies, some opportunities for rest and relaxation etc.
I believe it's important to remember that every new challenge your kids face, you face too. Myself, I have 2 teenagers (15yo boy and 17to old girl). I remind them that whatever they go through for the first time in life (certain milestones) I go through with them. If I have no clue as to what I'm doing, in the way of dealing with the challenge, this factor helps explain both my struggle and my lack of wisdom. We do our best to work things out together. We raise each other through challenge. I am who I am today largely because my kids have raised me to be a stronger, more intelligent and more reasonable. There is a reason for everything.
You are amazing :)