Don't yank school funding. Give her that at least. However, holding those strings, I might give her a timeline on family counseling. If at the end of three months she is unwilling to attend regular counseling with you/solo, you will need to renegotiate the terms of your financial support.
Regarding your mom, I would just be as straight as possible to both of them, then let it go. Are you and your ex on the same page? If so, continue to reiterate to Mom that you don't approve of her meddling and refuse to discuss it with her further. Period. Tell everyone in the family this is your position. Tell your daughter that you dislike her triangulation of relatives to get her way, but that you love her and are here for her when she's ready and that you really want to make things right. Then let it go. They're adults making decisions.
I posted recently about my meddling mother. Similar triangulation and manipulation issues in my family also. I just remind family that Mom isn't a reliable narrator, especially about me and my life, and I'm very straight with her about my boundaries. She responds well to embarrassment. Some of the things she does would be enough to get a restraining order if a stranger was doing them. I hear you. It's so painful when it's your mom doing the dirty work between you and your kids.