Let her save Columbia for law school. She should take on the least amount of Debt. Yes, they will ask for your income and assets for law school financial aid so you will not be off the hook. HYS Law only gives need based aid, not merit money. At least she will be able to take out loans in her own name for law school.
If you cannot/will not pay for Columbia, then it has to come off of the list.
Columbia gives a max of 16 credits for AP courses
https://bulletin.engineering.columbia.edu/advanced-placement