Should Mom be in a nursing home or have her home with nursing help?

Her dementia is only going to worsen and you have already said that you can't care for her 24/7 which is not humanly possible anyhow for one person to do without self-destructing. How far is her nursing home from you? Why do you feel that you have to be there every day? Why do you feel she should be home when it sounds like she is where she needs to be both for her care and safety as well as for your well being?

If she can afford three shifts of caregivers at home, then it might be worth a shot. But don't try this alone.

If she is in a nursing facility now leave her where she is and work with what you've got. They have an activities department and you don't have to wait for them to have an activity, with permission you can look through the activities yourself and see if you can find something your mom would enjoy. I'm sure it's very challenging since she is blind and deaf but she's where she should be. If you bring her home you will be responsible for her 24/7/365, doing the work 3 shifts of people do. If she's bored where she is she's certainly to be more so if she lives with you and as you said, she demands constant attention from you. That will be impossible to live with.

Have you spoken to the activities director about your mom's situation? Maybe she has some ideas on how to include your mom. But with your mom being blind and deaf it just may not be possible to find something that she will enjoy doing and that she will be capable of doing.