In writing? That wouldn’t be enough for me. I would want an iron clad account set up with the funds allocated solely for this kid’s college costs.
As the mom, do you plan to contribute anything towards college costs? Since right now she isn’t eligible for federally funded need based aid…that will likely be an expectation too.
I know you aren’t asking for this advice, but I think you, the mom, needs to see an immigration lawyer ASAP and get your immigration status straightened out too.