Been there…
Have you had a serious talk with your brother?
Next time there is an appointment have him take her. Even if she thinks you are going. Say you are simply unavailable.
Tell your brother that this is affecting your own life and you are struggling timewise , mentally and emotionally, and that when he pops in with shopping he needs to stop and chat with her.
Reticence to accept care is common. My Mum was a good, kind, v self sufficient unselfish Mum, but as her age and frailty grew remained adamant that they did not want carers, apparently oblivious to the huge amount of support we were giving.
In the end we just had to gang up and say ‘this is what is happening’.
The carers visits were originally moaned about (didn’t hang tea towels up properly, etc etc etc). But quite quickly became accepted and looked forward to.
Making Change is hard but well worth the effort. Be clear and resolute with your brother, develop a team approach.
Good luck!