Sister [24F] is demanding my parents [50s] and I [22M] owe her years of private school tuition, because I attended but she couldn't. What do I do?

So this is a really thorny issue right now. My sister is demanding my parents and I start a fund for her with all the money she's "owed" throughout her life. I don't know what to say.
Some background. My parents had sent both of us to private school starting in elementary school. After two years I had done well but my sister started acting up in middle school and got kicked out. The private school pretty much blacklisted her and told my parents they will no longer consider re-enrolling my sister ever. I even remember being dragged to some of these meetings last minute because my parents couldn't find a babysitter. That school hated her.
My parents looked at the remaining private schools and they weren't great. The second best school was a public charter school which is where they sent my sister. She did okayish here, got into some trouble, but never kicked out although she was always on the cusp of failing out because her grades got progressively terrible.
For university I got into a great private university and took out a bunch of loans to pay for myself. My sister got into a state college and my parents paid for all 4 years. I'd have thought this was enough to balance things out in her mind, but no.
We've both graduated now and my sister is suddenly demanding after so many years that my parents "repay" her for the years of public school that she had to endure while I went to private. She calculates almost 100k of school tuition that she's "owed." I think she's being absolutely ridiculous but she'll swear up and down to anyone that'll listen that my parents ruined her life because they favored me and only sent me to the exclusive, expensive schools. She never mentions that the schools THEMSELVES kicked her out, and my parents tried their best to get her into the second best school.
The issue is my mom has been fighting late-stage breast cancer for the past 2 years and mentally she's not all there anymore. She gets confused a lot and very emotional, so my sister's angry tantrums has had a huge toll on her. She now wants to dig into her and my dad's life savings to give sister this 100k to appease her. My dad is giving a firm "no" but he's also concerned about my mom who simply can't stand this much turmoil in the family or finger-pointing from my sister.
I hate my sister so much for being this entitled and deluded, but I don't know what I should do. She constantly posts on facebook about how all her friends are buying houses right now and she can't because of my parents (no effing idea how my parents keep her from buying a house...) and everyone believes her sob stories. She even told me that if my parents can't find the money, then it's my responsibility to find her this money. It's so ridiculously insane I don't know what to do anymore.
She knows my mom is weak and suggestible and I think what she's doing is cruel and selfish, but what can I do? How can I protect myself? Is there anyway I can still get through to my sister, or is she just a lost cause by now?

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tl;dr: Older sister went to several years of public school while I went to private, only because she was kicked out of the only good private school in our area. Now as adults she wants my parents to pay her 100k for the years of school she didn't have. My mom is sick and wants to go along with sister, but dad and I don't. How do we resolve this issue? Is my sister beyond reason?


Source.

Tell her to want in one hand and shlt in the other and see which one fills up first....