I know exactly what you are going through MrsJ. I'm in a similar situation with my 83 year old mother, who lives 50 miles away. Unfortunately, when people become old and have few activities or interests the smallest problem is magnified.
My mother just called me and has lost a Biro pen, she is getting into such a state about it, because the pen wasn't her's it belonged to one of her carers.
Like your mother, mine won't go to a day centre either. I've arranged for her to try two different ones, but she refuses to go back. Unlike yours, mine does live in Sheltered Accommodation, but it's only Warden assisted, so it makes no difference to her situation.
I've mentioned before, I'm trying to get her into a place with extra care, but where she will have her own living area, but have help and mental stimulation. Unfortunately, if your mother won't co-operate, there is little you can do. I know it's not easy.