How do I help my child. Trigger warning

Since I had my kids, I've always been the one taking care of them while my now ex husband worked. Once my kids found out my ex was cheating on me, all three of them started having bad feelings towards their father. Even after the divorce they want nothing to do with him. My youngest has been struggling the most out of the three and it's nothing to do with the divorce. She was bullied pretty bad at school to the point she was self harming herself. I seek help for her and she was hospitalized in a mental institution for a week. She since then has became so hateful. A child that once never met a stranger now refuses to leave home, barely attends her online private school, and expects me to do the work for her. When I explain to her, I can assist but not help she tells me, I'm a bad mother, I shouldn't have had unprotected sex and got pregnant with her. This poor child hates life so much and I don't know what to do to help her Bc I myself struggle with life and the "why me" daily. I've asked my ex to please help me out but to him he only wants their ss numbers to file on his taxes he even got that granted in the divorce, he even told me that if the kids move in with him for any length of time rather it be for the weekend (visits) or to give me a break (I have a lot of health issues) then he won't pay me the child support that I'm only getting ($400 for three kids). Every penny I receive with child support and alimony goes to my bills to keep lights, water, internet, and car going. I only got granted ($800 a month to take care of 4 of us) I'm not able to work at all right now. I have no friends what so ever nor family, just me and the kids. How can I help my child? I've tried therapy but that really didn't help her at all, I know she is going through a lot being 13, but how can I get her to see I'm doing everything in my power to help her I just can't do her school work for her? Advise please Bc I'm on my breaking point.