Hi Jup,
That is a difficult situation to be in and I'm sorry about your father's illness. It seems to me that you'll have trouble carrying on the way you are. I hope you can understand that your sister is stressed as well and that's probably why she blew up at you. But, the bottom line is you can only do what you can do and if I were you, I would guard my sobriety above all. That might sound selfish, but it was doing for others and spreading myself thin that led to depression and drinking for me. If I knew then what I know now, I would have taken care of myself.
Is it possible to hire someone (maybe a nearby teen) to help out with some of the errands?
I wish you well.
Love, Anna