M.B.
As I understand it (based on my own divorce), the divorce decree itself is what applies here. If there no mention of any financial support once the child turned 18 and the decree stated that child support ended when the child turned 18, then I don't think it can be enforced.
My decree for example states that my ex and I will share equally in college expenses including room and board, etc. However, the decree states that this ends if the child does not stay in college or no later than after 5 years of college. I also don't lose child support until my sons finish the year of school in which they turn 18.
My guess is that your hubby's ex-wife is hoping that your husband won't fight what she wants and thus agree to providing the financial support.
If your husband's decree states that child support ends when his daughter is 18, then this issue shouldn't really be between the ex and your husband - your husband should be talking to his daughter (who is an adult) as to his views and ability to provide her with financial support. My boyfriend is in a similar situation as he got divorced after his kids were adults and he didn't think to get anything about college or other expenses into the decree. They have worked things out such that he covers the kids' cars and helps with living expenses, half tuition, etc. while they're in college.
I think really the basis for the legal aspects are the divorce decree and the age at which a child is considered an adult in New York state. FWIW, this website states that child support must be provided until age 21:
https://newyorkchildsupport.com/custodial_parent_info.htm...
But, again, I think your husband's divorce decree supersedes that. Honestly, it would likely cost less than the airfare, hotel expenses, etc. for your husband to at least talk to a lawyer about this. Some lawyers offer free consultations. I would think your husband can also file for an extension for the court date (folks can easily do that on their own by sending a simple letter to the court). The most important thing is that your husband sign NOTHING until he has talked to a lawyer.