Weather - it's shit, it really is.
Normally I would say that your Sister has to lift her game and join in.
I live on the other side of the world to my family, and my DSis and my DBro do the caring. I have, though, flown over and stayed for a month at a time, even with young DC, and helped out. In fact I managed to do ' more' in some ways, than they could because I had a month of solid time to organise things (food deliveries, carers to come and help shower, equipment to be installed, different chairs to be brought in for them, car ferrying, interpreter services, cleaners, etc).
It is amazing the power of saying 'I am here for a month, I live on the other side of the world, my parents don't speak English, can we sort this out NOW while I am here'. (I simply didn't tell them there were others who did live there, didn't lie, just didn't share that with them!!!)
But by God it was hard, I spent every morning on the phone ringing agencies and badgering them about what sort of assistance they could offer, if they couldn't offer something, who could, did they have a contact that I could talk to, etc, etc.
My DSis and DBro had been chasing their tails ferrying my DParents from one appointment to another, taking time off, losing pay, that they just couldn't get ahead and the strain was showing.
Having that break for a month, me driving them to appointments etc was a fabulous respite (and my DSis and I are very close so just having the chance to natter constant was brilliant too). And getting ahead meant that some of the 'respite' was ongoing. DSis no longer had to run and do all the shopping for my DParents, as someone else does that now.
So I REALLY don't believe that living away gives an 'absent' child the ability to say 'sorry, there isn't anything I can do'.
They can organise internet shopping - she can ring and ask your DDad what they need ordering, talking it through, working out a basic shop, she can fly over every few months and the two of you sort out the next steps, etc. There is LOTS she could do and its shit that she doesn't.
BUT...... you're not in the standard situation. You've grown up in an abusive background, and even though your DSis wasn't 'abused', she probably did suffer. I'm guessing she was the golden child and she has her own burden to bear.
Its not fair that you have to carry the burden and responsibility of caring for such shit parents. You need to focus on yourself. If your Dad tries to tell you something and instructs you not to tell your DSister just say 'no dad, I will not be keeping this to myself. You need to tell us both'.