Well, when my grand-mother was in he early 90's she also got to a point where she was unable to care fir herself in her apartment and me being the former social worker, my parents asked for my advice...
...which was to have a social worker be the fall guy...
Your mom just wants to have some control of her life and maybe it's best for the socail worker to say, "Look, Mrs. ___________, we have inspected your house and it just no longer is fir to meet your ful;l time needs. Lets loot at some alternatives here."
One may be to keep mom's old house without the heat and let her "visit" there during the day time... But be sure to have several ideas out there so that mom will be part of the equation..
Now if she her reasoning skills have deteriorated too far then maybe fewer options or options that may seem different to her in presentation yet are very similar under the sugar coating...