Dealing with my 104 year old mom who fell again and is now at a rehab, advice?

Wow 104 years old. That's remarkable. She will ask you to take her out of the rehab though, so be ready for it. If she's still with it enough to understand and she asks you to take her home, tell her the truth.
That you'd love to but because she can't walk or stand right now, she can't be cared for properly at home. Tell her that the rehab is only temporary until she's strong enough to go home. Even if none of this is true and she's going to be living the rest of her life in a care facility. It will make her feel better in the moment, and really what else counts when a person is 104 other than feeling better in the moment?

What has changed since you last wrote in Jan 2020? Is your mother still living in her own home, with you on a short leash? (Your profile says that she lives in your home, so it's a little confusing...is she now living with you?)

You wrote that the two facilities in town had no room. Are you still trying to get her into a facility? This could be your chance, since she's in rehab.

Give her all the sympathy you can muster, IMO it's only natural to want to get out of that situation and go home (especially if on some level she is aware that she is unlikely to ever live independently again).

I'm sure they have ways of getting difficult patients to comply. My mom would always behave well for the PT/OT people in rehab and act like a whiny baby if I asked her to do anything that they asked. So, their advice for you to leave might be the best. She shouldn't come home until she is at a certain level physically and I doubt she is there yet. I would tell my mom she needed to be able to get into the car, into the house, and walk from her room to the bathroom without assistance. So she needed rehab until those things became easy again (after knee replacements).

My mom and MIL always complained about the facilities and the food, etc. Some just love to complain, it seems.

If it were me, I would let her know if she can't do X and Y, she will unfortunately have to go into a facility. Maybe that will be an incentive? "Sorry mom, but it would just not be safe for you to come home if you can't stand or walk." End of story. She will not like it but she does not have to like it. It's reasonable that she cooperate with rehab and improve her condition. Unless sitting in a bed in a nursing home for the rest of her life is OK with her. Which I highly doubt, but you never know.

"My mother who is 104 years old fell again last thursday night. We took her to the hospital where she was found to be anemic, have low kidney function, and had a bad UTI. That didn't explain why she was unable to walk or stand on her own".

You don't understand how having a UTI, poor kidney function and anemia can add up to not being able to stand or walk? Added on to being 104?

I agree with the nurse. Let your mom be in rehab. Let them handle her.

If they complain about her behavior, ask for a geriatric psych consult.

If you are going to be a caregiver to this 104 year old lady at home, you need to have visiting health care coming in regularly to do blood work and skin checks.

Think aboout the idea that this might be the time to permanently place her.