92-year-old living in alone in her own home. Her closest child lives 4 hours away but continues to adapt to alternative housing. Should we get a case manager?

Is there some dementia?
If not, no matter the advanced age, you cannot interfere.
I don't know if there is an active POA here? A concerned MD communicating with family?

I would call APS for wellness check if you are concerned.
I think that you and Siser may need to visit and assess this situation for safety.
If this is an unsafe situation for an uncooperative elder you have a world of woe ahead.
What most often happens, and we have seen it happen here particularly with one former Forum member I can remember, is that there are attempts over and over and over again, and the same number of refusals.
The elder did go down at home, and despite checking coming quickly it was not quickly enough. A fall can bring death on with great rapidity.
While our Forum member felt dreadful, we all here had witnessed her attempts to intervene.

In truth, at this age? It's an option to die at home unaided. To be honest, I am saying that as an 81 year old ex-RN. It's an option. One that will surely break our famiy's hearts, but an option.

I had to wait it out — twice, It’s was awful waiting but was necessary. Both parents who are now in a NH and will be 96 refused to consider leaving their home.

After a health event your mother will go to the ER and you tell the social worker that she lives alone and this is an unsafe discharge.

You would need to inform your mother that if she insists on going home she is on her own coordinating her travel and setting up her own care. I had to do that with my mother who was demanding to leave rehab,

Good luck. This is not easy. I feel for you.

A case manager will only work if your mother will cooperate with their efforts. You may luck out with a case manager with enough experience that some “tricks of the trade” may help. Otherwise you’re in the club of many here, waiting for the fall. Also stated as “events will happen that will force change” Many of us have waited out the events, it’s no fun, but it inevitably happens, and it’s then that changes can effectively be made. Sorry you’re likely in the club