D3 merit would have to be in line with other non-athlete students receiving either need based aid or merit aid. And yes, the NCAA does check these things.
You need to ask the coaches directly if there is enough merit money at the school to make it work for your family. My daughter was being recruited by a lot of D3 schools and I asked directly. Usually the answer was no, that she’d not receive enough money to make it work.
Are you sure you will get enough at a D2 or NAIA school? At a d1, it would be a full scholarship for basketball, but the full rides are pretty rare at D2 and NAIA, even for basketball and football players. Mixing merit and athlete aid is more common in D2, but then you lose need based aid from the school.