How do you get a senior who resists to attend a nursing home? What is the cost?

She is from Euclid, Ohio. Every three months I would drive to Ohio to take her for her doctor's visits. Her last visit was in October 2015. She weighed 80 lbs. and her doctor recommended she move in with her daughters because of her progressing dementia. She feels her time here is over and she wants to go home. There is no one there to look in on her so I have refused to take her home. She has become physically aggressive, she claims we are trying to poison her and throws good food in the garbage. I fix the same foods for her, my husband and I. She does not believe I am her daughter and she constantly makes all kinds of accusations. I am not sure what to do and I wonder if this program is good for her or should I be considering a nursing home? Please help!