Does mother have to drain all their funds before qualifying for Medicaid?

Not all, no. For a single person, applying for Medicaid can be pretty straight-forward, especially if there are few assets.

For a married person it can get way more complicated fast. I endorse Babalou's advice. See an attorney specializing in Elder Law. It will cost Mom, but a mistake could cost her lots more.

No. Your mother needs to see a certified elder care attorney so that she (and you) can better understand the rights of the "community spouse" the one who is not in the nh. Do this as soon as possible.