What do you do when your mother keeps saying she is going home no matter what

My mother 84 yrs old broke her leg at home from falls which she has been having for about 3 years now. Every time she has fallen she refused to go to the hospital, take care of herself or the house. She would not let us hire someone to clean her house, do repairs and the only thing she did was sit in bed to watch TV. She is in a nursing home which she has fallen 2 more times there and my brother and I both agree she cannot live on her own any longer but she keeps saying I am going home no one is keeping me here. She said she is going to sign herself out but she will end up falling again because you can see she is not herself since the broken leg accident. What can we do to keep her in the nursing home for her safety? I have medical power of attorney. Everyone keeps telling me there is nothing we can do that only the doctor and suggest she stay in the nursing home. We know she will hurt herself bad if we allow her to go back home. What grounds as her children do we have to make her stay there. Thanks really need advice with all of this.