As much as I despise what the ex is doing (and as much as I absolutely understand, as a stepmother with a bad "ex" situation), I would not threaten her. I would not tell her I'm going to report her.
The divorce agreement says all 3 are to contribute - father, mother, daughter. Your husband hopefully has been planning on this. The daughter needs to get a job and start going through all the paperwork necessary for financial aid (FAFSA, loans, scholarship applications from every single source). Your husband can tell his daughter and his ex what his contribution is, and that's it. The mother will have to fill out forms and provide copies of her tax returns. If she doesn't have them, that's her problem. Your husband isn't requiring this, the "system" is - and that's the system she's supposedly so good at working.
All parties should attend the college-prep nights at the high school, meet with the guidance counselor, and so on, to determine what the family can afford. Your husband is under no obligation to foot the bill because the others don't live up to their agreement. Do not raise the issue of your other children - let your husband handle this with his daughter and his ex.
I'm not sure if the divorce agreement says what percentage the kid has to pay - is it 1/3 - 1/3 - 1/3? Or 40% dad, 40% mom, 20% kid? Or just vague?
Hardly anyone can afford the cost of private colleges anymore - so there are extensive networks of aid packages from the government, private organizations in your daughter's town, and student loans that she can pay off when she graduates. It's time for her to get busy, seek out funding sources, and start applying, writing essays, and making herself look worthy of these awards.
Your job is to be encouraging and perhaps send her some links. Otherwise, stay out of it. It will backfire and make you look like you are choosing your children over her - that will NOT be good for anyone.