Why won't my sister help more with our dying mother?

Glow, please note that not everyone is cut out to be a caregiver even if they aren't employed. https://www.agingcare.com/articles/not-everyone-cut-out-to-be-a-caregiver-162192.htm

I was one of those people, couldn't be hands-on, but I was good with logistical stuff. Since I was dual Power of Attorney, I was able to take over my Dad's finances, thus write checks for his bills, and watch over his accounts. I also could take Dad to his doctor appointments, haircuts, get him groceries, etc. Maybe your sister could help with those things. Something to think about.