This is really surprising and wrong for the older sister and her husband to treat her biological mother that way. Even if her mother has offended her in some way, it does not guarantee her to treat her mother like that especially in that sick state of hers sef. It's really annoying as you said.
I can bear to keep a cool head whenever my mum is being treated in that manner and as such, I respect every mother and don't take it likely with people treating their parents like that, whether I know you or not, I try to give a piece of mind.
Older brothers especially, first born are always burden with this kind of responsibility, and most times it is unbearable. I pray thinks work out for him and also pray for good health for the mother.
Thank you for sharing @bipolar95