I agree that your sister sounds like she’s a narcissistic personality, the things she says and does, the extremely selfish, everything is always me me me, manipulative, grabby, she’s the constant victim, gaslighting, lying, covering things out of shame that dents her ego, her generally being life sucking force who makes everyone around her miserable and she takes takes takes, and it always comes back around to her, wants everything handed to her without ever earning it, nor being grateful, nor having insight into her impact on others, her lack of empathy, and her never changing or growing out of things, you’re treading on eggshells because you know that even the smallest comments or perceived slights she blows up at. That in itself is a manipulative tactic so that people learn not do do that again to her.
You wondered why she thinks and acts certain ways, but all these things your sister says and does are very likely caused by the narcissism. There are more than one type, but they pretty much are all on the same script.
Please go online to youtube and search for Dr Ramani. She’s a professional psychiatrist and is a leading expert on this very personality type and dedicates a lot of her time to educating people on how to understand why they do what they do, and how to make things better for you to cope with, and what to do or not to do or say that would make things worse.
I can’t recommend her and her videos enough. They’re all fairly short 8-12 minutes long, clearly titled and it’s extremely eye opening, educational and life changing help for some people suffering with these people in their lives. Although we can’t change them, by education you learn the tools needed to keep your emotional suffering to a minimum, to keep you safe, and how best to engage with them. Just knowing WHY they do what they do can at least be validating, and there’s loads of support on the comments sections from others who have this type of person in their own lives too.
I am sorry you and your parents are going through this, and hope that there’s some useful information, and advice that will help ease the burden.