Hire a carer for overnights. Live in help.
Remember, if your kids are older than 8 or so, they are learning how to care for you when you are old and maybe cross or difficult or depressed.
It sounds like making a visit and both you and your sister sitting down with a counselor is a good idea. Can you find a grief/family counselor through her parish?
The idea of building an apartment at your sister’s place sounds perfect. Now it is a matter of finding out why she fears your sister using it as an income source when she is gone (to me, that may be simply a way she is fearing her own death, that she will be forgotten after she dies).
Perhaps, does your sis have kids? Does auntie like those kids? Maybe a promise that any money made from the unit after auntie passes will go toward the kids’ education? Or that they will make a donation every month in her name to the parish?
My gut says this is about being forgotten. Realizing that she has no children and that when she is gone, that is all to her branch of the family. Heck, we have an only child and he will never have children. I often feel sad that we will have no heritage, I have no one to pass things on to except to grand nieces and nephews and I don’t know that they will even want them. I could easily BE your Auntie in another 30 years.