My mother has medical and medicare. Can she use this towards her stay there?

I don't know. I go there to use the gym especially the pool.

Can you use the pool for day use

It will depend on what kind of care she's getting. If she's in independent living or assisted living, MediCal and Medicare do not cover those services. If she is in the nursing facility, Medicare will cover that for a short period of time--something like 14 days (I forget the exact number).

Call and ask.