The issue of whether she has dementia is important. It's possible she makes bad decisions with no dementia at all. But if she has dementia, it will get worse until the day she dies, and the unpleasant fact is her finances will be better if you run them.
The way you find out is to convince her to visit a psychologist who specializes in testing this. Their fee is several hundred dollars and the test takes several hours. They issue a report a couple weeks later that gives details and can, if necessary, be used in court.
My dad got Alzheimer's. My sister and I, thanks to arranging Power of Attorney paperwork before full dementia, eventually took over his affairs. We did this after researching Alzheimers on Google and reading a couple of how-to books that were very helpful. It worked out very well in the end but it was a lot of work. I view it as repayment for his having raised me when I was not competent. But since it's a lot of work and your relationship is already strained, I suggest asking yourself the following question: How bad will it be if you do nothing?
Then ask yourself: Can I accept the consequences of doing nothing?
If the answer to second question is yes, do nothing. Focus on being friendly, and hope the comfort you give means something to her. If the answer to the second question is no, then duty calls and you're better off facing the music ASAP. If so:
Legally, you can't force her into anything except by court order. Your options are:
1. Sweet talk her into accepting your advice. She follows it and all is well.
2. Persuade her to give you financial power of attorney. Use it to pay her bills - the income all goes through accounts that she can't access any more, you access them instead. Invest the annuity more wisely. Give her a day to day allowance (via prepaid cards, cash, small checking account, whatever you think best) until that is no longer practical. We got him to sign the POA on the basis that it wouldn't take effect "until a doctor says so", meaning until a doctor (a doctor of psychology, as in the test above) gave a professional opinion that he wasn't competent. Note that signing the POA required him to meet privately with the POA attorney. I think the attorney recognized the situation and gently guided him to sign. The psychologist ruled Dad incompetent as soon as he was tested.
2b. If you get financial POA, I suggest arranging medical POA also if the cause is dementia, because she won't handle her medical decisions properly either so you're probably going to end up going to the doctor with her too. My sister used all her sick time on Dad. I would have too except I quit working and became the lead doctor visit chauffeur/decision maker. Yep, time consuming.
3. If she won't listen and you must intervene, you get a lawyer, who files a petition in court seeking guardianship. You are asking the court to become your mother's guardian against her will. This requires persuading the court she is incompetent, a tough bar even if you feel she is clueless. If you win in court, same results as 2 and 2b, plus she's even madder at you whenever she understands what is happening. (Whenever I would blame the court for something, Dad would say, "You tell that judge to shove it up his ass!" The joys of being the guardian.)
