25, I like the letter. I think it was reasonable and generous. I think you're already at last resort stage, considering the timing. I hope your in-laws are generous and helpful. I wouldn't count on it, but I think you would regret it if you didn't send the letter and your D19 had to drop out of school.
I also wouldn't delay sending it because it is hard to say what actions they might need to take to get the amount of cash that is needed to get her registered.
I would also ask if there is some kind of payment program at your D19's school? I know that my university had one that was not need-based. You might pay a slight up charge spreading the payments out over the term rather than paying the lump at registration time, but the advantages would be: 1) the amount of money you need to ask the in-laws for could be reduced; 2) it buys you time to get your STBX to pay his share or start paying you the support he owes; 3) perhaps your D19 can get a job to pay a portion of it in the event that you end up having to pay her tuition.
In my state, I was told by my lawyers that the courts can't compel a parent to pay for college. I've been trying to prepare myself to pay for it on my own, knowing Mr. Fantastic's spending habits. I hope you can find a good solution for your D19 and that she doesn't end up having to eat a sh!t sandwich.
You've been doing marvelously, considering the chain of events you've been working with. I hope you feel very proud of yourself.
Me42, H40 D12, S8, S7 A revealed: 7/13 Sep 4/14; Agreed to D 1/15