A friend told me my mother has what's called "failure to thrive"; would moving her to a nursing home be the right choice?

The doctor says there is very little physically wrong with her other than slightly high blood pressure and fluid retention, but she has does have dementia. I had to take her from her apartment into my home because she was falling and not able to care for herself in general. She didn't want to comb her hair or wash, and the apartment smelled strongly of urine. I was meeting all her needs (shopping, cleaning, washing clothers, etc.) She did not want to go out or do anything, and she wasn't eating properly. Since she's been living with me, she's eating better and she's clean, but she's extremely apathetic and still doesn't want to go out or do anything more strenuous than watch TV in bed. I've gotten her a word search book, but she no longer can do it or even use the phone. I have companions come in 21 hours a week, and that helps give her some social time. Due to the dementia, she thinks my adult daughter has stolen from her, and has cut off ties to her and my granddaughter. She was blunt, somewhat cold and could be difficult even in the best of times, so there are no other people that want to visit her, leaving only me. We were never really close, so I find it hard to be close to her now in this situation. I'm a very good caregiver, so her physical needs are more than met, but I really don't know what to do with her on an emotional level. It seems that she has no interest in talking or interacting with me, and comes out of her room mostly when my husband and I leave the house. My friend works in a local facility that's has assisted living, nursing home, hospice, etc. and keeps suggesting that this would be a good idea for my mother because of the activities and socialization. I had never heard of failure to thrive, but it seems as if that might be what's happening. My mother was a very independant person, and now that she's dependant on me, it's like she's just given up. Would anyone have any ideas about this. Even though we don't have the typical mother/daughter relationship, my mother was a good responsible parent and raised me to the best of her ability. I want to do what's best for her, so the thought of her wasting away in her bedroom scares me. Would a high quality facility like the one my friend works at be a good idea?