We had a similar problem with FIL
He accepted (to our amazement) a carer coming in to give him his tablets once a day but would not let the same lady make him as much as a cup of tea then or when she came back later to try and make him a meal. Social services were very good and the girls tried for something like 4 or 5 weeks with afternoon visits to get him something to eat and he simply refused. A couple of times they tried to push it by trying to open a tin of soup for him but he got so upset with them they had to give up.
He was
literally living on marmalade sandwiches and 'tea' at this point. We went over to visit and make him a meal once a week and a neighbour would give him something probably once or twice a week as well but he simply would not accept anything else.
Sadly it took him falling and a hospital visit to find out how bad he actually was (living in the same clothes day and night, not washing and verging on totally incontinent, very unstable on his feet, absolutely no sense of date or time and realistically no sense of understanding of the world around him and thus no sense of risk or danger). He went straight from the hospital into a home - much to our relief I must say.
What amazed us was that he didn't have the problems we expected when he was in the home. We expected all the demands to go home, complaints about the carers interfering etc etc. and didn't get a cheap
That was why we had held off trying to put him in a home because we expected he would fight it and then nothing...
The only explanation that we could come up with was that the familiarity of his home triggered thoughts that he could (should) do things whereas without those visual triggers he accepted help.
Your Mum sounds a bit more "with it" than FIL was by that point but if she won't accept help at home unfortunately she might end up in a home sooner than might otherwise be the case
Good luck getting something sorted out.