Patty, You do seem to be very strong and I'm sorry your sister isn't as strong so that she can help. I suspect she is in great pain and denial of your mom's terminal state of health. That's part of grief and it is different for each of us. Included in there is our own comfort or discomfort about our own mortality.
I understand your frustration though because you need help, your mom needs help, and your sister seems to be available. Maybe she could come 'learn' how to help by being there when you are and then could eventually do it alone. I know your mom's time may be short and that's certainly a consideration.
Could she then help you with the cost of having qualified and loving caretakers come in to help?

for you and your mom, and your sister too.