Sympathies OP. My situation is that I am caring for 90yo DF. Sis lives in Europe so is not on hand, but she is very quick with the accusations.
DF had a fall 18 months ago. Until then he managed on his own pretty well. I dropped everything, took some unpaid leave and went to stay with him 230 miles away until he was stable and then brought him back to stay with me and DH so I could get back to work. This is now the new "normal". I shop for him, do his laundry, life admin, cook dinner and take him out. He does his own breakfast and lunch most days. I have kept her in the loop about everything but she has thrown so many accusations in my direction that I cannot take any more.
In the last 18 months, she has spent less than 4 weeks looking after him. She has apparently put a flag on his POA so that my adult DDs cannot be added as deputies, despite us receiving professional advice to say it was a good idea. I have repeatedly told her that she can see him whenever she likes but at his place, not mine. She tells anyone that his flat is full of mould, so much so that she cannot possibly stay there with him. There was some condensation, which has now gone and I have cleaned everything up. She and her moronic husband are angling to spend time at my home, which will not happen. DF's brother and family get it and have been amazing. Nice aunt says that my DF looks really well and I'm doing a great job. DF's sister thinks the sun shines out of my sister's arse and that she can do no wrong and that I am the villain. I am the older sibling and she has always resented this.
My way of dealing with her is to communicate by WhatsApp. When she goes off on one, I mute it. However, I can save her tirades as evidence of her lunacy. When she starts, I type up what I want to say on my laptop, then leave it for a while. I find responding in the moment is futile and gives her what she wants, so I now stick to cold hard facts only. If I take Dad out somewhere or we do something nice, I send her a photo with a one-line caption e.g. "had a BBQ" with smiling DF holding a glass of wine. It shows her he's still alive and enjoying himself and she cannot then accuse me of keeping her out of the loop. I also ask her opinion on mundane things like: "we need to sell Dad's car, any suggestions?" They are normally so off-the-wall that I do what DF and I have already decided, but it looks like she has been included, so her accusations can be disproven.
Sorry this is so long, but I do share your pain. If annoying sis is giving lists, she has to accept that you will do things in the way you consider to be in DM's best interests. If she sees it differently, she needs to do the task. End of. She cannot have it both ways. I have also said to mine that she might not like the way I have done something, but at every stage the decision I have taken has been in DF's best interests. If she has an issue, she can contact SS. Good luck!