When is it legal to assume power of attorney? Who makes that decision? How do you know when it is time to do so?

My mother is 81. She has been diagnosed with Alzheimer's and dementia. She lives alone and I am very concerned about her. Although she can take care of her basic needs her memory is failing. She is forgetting to pay bills and her children are asking her to lend them money. Her checkbook is an absolute disaster, with voided checks and crossed out entries. She has burned several tea pots, and has gotten lost in her neighborhood. She is also a smoker. Her doctor has repeatedly told her she should not be living on her own. I am very concerned with her welfare and have tried to talk her into selling her house and moving in with me or one of her other children, some of whom are parasites. She said she wants to die in her own home and refuses to leave. I want to honor her independence but feel it may be time to intercede. I love her dearly and don't want to force her to do anything. I am the executor of the will and will have power of attorney when the time comes. I am also very worried about being legally responsible for her welfare. I have no answers but many questions. When is it time to make the big decision? I am in dire need of some instruction, please help me........