Mom is receiving spousal A&A. She is living in an assisted living facility but recently hospitalized. What happens to her benefit?

Nothing that I know of. If she is getting it because she is in an AL, and she loses her room because of an extended stay, then maybe a problem. But one week? Don't see a problem there.

The only time she loses her benefit is if she ends up needing Medicaid to pay for her care. You can't have both.