How do I get my mom to accept being in a nursing home?

Get her a talking clock to acclimate her to the time and the date, and day of the week.
Be there for her during the evening hours, or late afternoons consistently, talk to her, read books to her, say goodnight, say when you will be back.

Ask someone to answer her when she is calling out for help. You can prepare a script and post it so an aide can reassure her when you are not there.

When I visited a patient in a nursing home, she was repetively calling out
"I'm hungry". I looked over around the curtain, and said I will go get someone to help you. Someone will be coming shortly.
She stopped calling out. I told a nurse on the way out who explained that is common, but they will check in on her.
The patient that I was visiting motioned no, shhhh, don't speak to her. What was wrong with giving her neighbor a moment's peace from calling out, I just don't understand. I speak to strangers in need. So sue me.

I've thought about rerun tapes of their long time favorite shows too. But there's still a lack of hands on activities...he doesn't like child/like games they do there,

My dad is in AL, legally blind, and most activities they do there he can't participate in...sad to see him just sitting there, listening.
He does love his old country music though!!!

Would your mom like or be comforted by a baby doll or a stuffed animal to hold? Sometimes others will want to comment on her doll or stuffed animal and it might prompt them to speak to her. It could possibly be attached to her wheel chair so she could find it easily and retrieve it if she drops it. I'm not sure if this is a good idea or not. Just trying to brainstorm with you.

There is a documentary about music and the relation to dementia sufferers.  I can't remember the name right now. In the documentary, the man gives iPods (any generic MP3 will do...) with headphones to dementia patients, and the iPods have music from their younger years programmed on them. The elderly seem captivated and uplifted by it. It shouldn't be that difficult of a documentary to find with the description I've given. Google it, watch it, see if that wouldn't be something to help "keep company" for your mom. Had I known about it when my grandmother was still alive, I would've tried it, and I think she would've loved it.  

Hey! I found one of your posts! What I did for my blind grandmother in same situation was get her earwax cleaned out (very important) and bought basic hearing aids for her. (If you're interested in how to get an inexpensive hearing aid that works, let me know, I'll tell you what I bought for her, and they did work for her.)

When she could hear things around her better, she didn't feel so alone. I could reassure her from the other room that I was right there. Your mom may be able to experience the same reassurance if she can hear better, but I don't want to get your hopes up because it sounds like your mom is declining because losing weight like that isn't good for elders.  :-/  I want her to have as much comfort as she can, though, and there are a few things that you can try.

There are things called "fidget mats," for people who can't see, to play with in their laps. I've never seen one in person, but it seems like something my grandmother would have liked.

Can you ask the staff that whenever they go by mom's room, that they give her a piece of her favorite hard candy? At this stage, it won't hurt her any, and my grandmother loved it. Keeping a big candy bowl full in her room, asking staff to give her a piece... it could help to give her a moment of fun in her day.

Those are my thoughts at the moment. I hope AC group can come up with more ideas for you. :)

Unfortunately I have no experience in this situation, but I can bump this question to the top. Sorry it seems to have been overlooked.

If you have the funds, you might try hiring a companion for a few hours a day to keep her company. Is your mother bedridden? Perhaps the companion could take her for walks (using the wheelchair if needed) or read to her. What kinds of activities did she do at home?