How can I get my homebound mother an ID?

I would go to the office myself and ask them this.

I wonder what sort of ID your Mom now requires. If she is not flying anywhere she can likely use her old ID, birth certificate, whatever for any needs? I know I made the mistake of taking an OLD driver's license to the airport and they still let me fly.

Best info will come from your local office, so access them.

Someone needs to take her to the DMV. She will need an ID for the bank. My daddys DRS Lic expired and the bank would not allow him to access his account without a valid ID. Thank God my name was on the account and he was always with me when he went to the bank. So I would just show mine. I finally got him to the DMV and got him a state ID (no drivers lic).

At this point why does your mom even need a state ID?
My late husband drivers license expired in 2015, and I never took him to get a state ID. His doctors office which was the only place that ever asked for a picture ID, gladly accepted his expired license until his death in 2020.
So I'm not sure that I would worry about getting her one unless she doesn't have an expired license to use.

Did she ever have a driver's license? Depending on the state she lives in, that can be converted to an ID. Ask your DMV.