She is 93 and has moderate dementia. She forgets to use her walker and is up and about the moment I am out of the room. She complains about having nothing to do and wants to help me with my household and yard chores, but there isn't that much she can physically do. She won't visit the Senior Center, refuses all hobby suggestions and is unhappy with her situation.
Was she always a busy person one who lived by the philosophy that "Satan finds work for idle hands"?
What kind of things did she used to like? Maybe she liked to knit. So get her some big needles and a ball of thick cotton yarn and have her make dishcloths. Put a basket on her walker and put some cleaning supplies in it and ask her to do something in an area where you are not trying to get stuff done. "Mom the dining room table looks dusty. Would you mind polishing it"? "The glass on the back door has muddy footprints on it.Could you clean them off?" Out in the garden give her a little patch and either some flower plants or maybe a tomato plant to take care of. Given her age you can't be young yourself so don't let her tire you out. Accept the fact that she may fall and injure herself and that you will deal with the consequences if and when that happens but for now don't wrap her in cotton wool.
Good of you to take care of your mom. I would also suggest giving her a craft table. Maybe find large piece puzzle for her. Leaving the TV on or a movie on for her. Are there any family or friends who could come to visit while you are doing your chores to give her some company?
I know you mentioned she doesn't like going to a senior's centre, but maybe just take care and leave her there for day. She might find she enjoys it once she is there.
Can she match up sock and pair them off?
Give her a deck of cards and ask her to separate black fro red cards.
Can she sort coins?
Any of these busy tasks will keep her busy for a while.