I went through this with daughter, she went through the terrible teens from 13-17, was not pretty. Me & her dad had joint custody, then she left her dads and moved solely with me, didn't like my rules, left my home for my parents, I begged them not to take her in, but they did, that didn't last long they kicked her out, so she went to her friends house and that didn't last long(even though the mom was easy going & it was a flop house, she was an extra body that she couldn't look after) during all of this I had her in councelling with cdc and finally she came back and then to her dad's, and now is easy child, 20 and in college, graduated with honors, health nut, and a joy to be with♥ But.....it was rough for a long time, at one of her suspensions from high school I decided I would home school her, the twins were babies(so think of teen stress + looking after 2 premature babies), daughter BEGGED me to let her go back to school, the school BEGGED me to give her one more chance, so we did. There were still bumps and bruises along the way but we muddled through and I couldn't be more proud of her.
Do not pay child support, your daughter has a home, you didn't kick her out and if this women wants to let her live there than she can pay for her too. I wouldn't give her one dime. You can't afford her, then send her home and don't offer what you can't give. Just my 2 cents.