Hi dear Maddie ~ I'm sorry I didn't see this before. I would have replied much sooner!
Yes, she might ask you to take her home. Was she extremely non-functioning when she was home or was it off and on? Could she do every-day things at home? If she got very confused, etc when she was home, perhaps you could remind her of how things used to be when she was on her own. Remind her of things that happened (if that's not a dangerous thing to do, both for her and for you). Gently convince her that where she is, she'll have friends and people to take care of her, etc. Sure, it will be hard and she might be argumentative but you have no other choice, bless your heart.
I can't imagine how you must feel. My ex-sister-in-law is psychotic and lives in an adult foster care home. When she first went over the edge, she went after my inlaws with a butcher knife!!! She was committed to a hospital at that time. Now she's much better but will never be able to live on her own ~ she's 56. She had adapted nicely where she is and never asks to get out. But I know your case is different ~ this is your MOM!
I guess all you can do is love her, be gentle with her, and be firm. God bless you. My heart goes out to you dearheart. Peace, Lee