OP, no one deserves to have to live with vermin in what is essentially their bedroom / hospital room. It is perfectly reasonable to draw a hard line at not wanting to be in a facility having a rodent infestation in patient rooms. I agree with PP that this facility should stop accepting new patients until they can get everything figured out.
This facility can and should do better. My dad was in the Wasserman building last year. The mice issue is a known problem to at least 2023. Ring house apparently is dealing with this same issue.
My dad raised his concerns about the mice in his room on the second day he was there, citing his discomfort with seeing rodents in his bedroom. The doctor doing his initial assessment chuckled and told my dad "Oh, you'll get used to it." Well, dad was not happy about that, and like OP's mom, asked to transfer to a different facility, which he did.
OP if you are still reading, it took us making multiple phone calls over a few days, doing a little bit of extra paperwork and a further day of effort making sure Medicare would approve the transfer to a different facility, but I am glad we did. When I went into Hebrew House to see my dad, once I got upstairs from the public elevator lobby I was not impressed. It is hot and stuffy. Everything is dingy and wearing out. The rehab facility is new and nice, but, patient rooms are tired looking and the hallways were cluttered with food carts, probably attracting the mice.
My impression is they are under-resourcing building janitorial services and pest control, especially if the problem has gotten to this level. Mice breed frequently, it is a matter of time before the whole place is overrun. Get out while you can.