She also refuses live-in help or to live with anyone else? POA has medical and financial POA. Mom is unable to cook, clean and needs assistance with daily living. She has people come and bring food or take her out to eat. What can be done to get her into a facility?
If so it no longer matters if she agrees to go, you come up with a creative solution to move her. Start with talking to her primary doctor about medication for anxiety, depression or agitation. Then work with the facility admins on a plan to get her there.
You might have to pay extra for a caregiver to be with her 24/7 the first couple of days, to help her get oriented and calm her down, as best as possible. Talk to the facility; they might have staff who do this, or they can recommend an agency that they use.
It won't be easy but it will be best for her in the long run.