Been there, done that with my two siblings. My sister does visit the home once a week or so yet my brother barely sees her, then again he has been consistently like that throughout the last thirty years.
One thing is for sure you and your brothers very different relationships with your mum when she was well probably in some way influences your different responses to her illness.
I was always the closest to my mum as a child and an adult as she and my late dad cared for our children while I worked, so the close bond was kept. My husbands parents died a long time ago too, so he looked on them as surrogate parents from early in our marriage, all these factors must affect how we deal with this horrible disease that takes away the ones we love in such a cruel way.
The way I deal with it as I did from the the day my wonderful dad died recently is to focus on mum and try my best to see she is well cared for and to visit as often as I can, which is difficult I know with work and family commitments. if your brothers' don't want to, that is their choice and no amount of anger in you is going to alter that, so please let it go.
I love my mum very much and I know somewhere inside she loves me too, even if she doesn't know who I am most of the time, she is still and always will be my lovely funny mum.
Chin up
Kathleen