I have absolutely no advice, I can only sympathise.
My grandmother died last year and prior to that she spent a decade in and out of hospital and was increasingly frail.
My mother visited her twice weekly - drove there after work.
My brother lived with my mother for much of that time and when he didn't he lived near to my grandma's house and the hospital she was frequently admitted to.
When he lived with my mother, who has a car, she drove them both over. When he didn't, he lived a 25 minute bus journey/10 minute drive away.
I was a lone parent of a toddler when it started. I caught two trains a day to university in another city and then 2 back again. Every day. I didn't have access to a car. And my grandma lived 2 buses and over an hour away.
No one ever offered to drive me over to see my grandma, no one offered to look after DS while I went.
I physically didn't have the energy, practically didn't have the means and logistically didn't have the time to visit more than I did.
They didn't understand. All they could see was the burden of responsibility they felt and the sense that the pressure on them would be relieved if only I did my 'fair share'. Unfortunately, it's not always that simple.
It's stressful for all of you.
Your sister feels the responsibility, you feel the guilt.