Concerned

Trying to parse this. But here are a few thoughts off the top of my head.

* Yeah, it would be lovely if your aunt could have the mortgage all paid off before she dies. But that's most likely unrealistic. If your aunt is like a lot of sick elderly folks, she probably doesn't have a lot of extra $$ just lying around to pay extra on a mortgage. In the choice between extra $$ on the mortgage and food or meds, guess which need will be the last one on the list? This whole thing is like vultures circling.
* If anyone in the family has decided that your mother (or, perhaps, you) should be the ones to pay off the aunt's mortgage, then the proper response is, "You first." And if that doesn't work, tell them to go pound sand. Seriously. Your mom is under no obligation to rescue her sister's financials. Ever.
* The caregiver is clearly terrible and should be replaced. Professional caregivers are expensive. A reputable home with 24/7 care might be a little better in terms of cost, and it's more likely to be better with late night and weekend coverage. People using caregiver agencies can sometimes have to deal with caregivers not showing up at their shifts on time or not giving meds or meals. In the US (don't know if you're in the US, of course), this industry is particularly poorly regulated. But nursing homes and caregiver agencies at least have deeper pockets, so if it comes down to you having to sue them, you're more likely to recover something, anything, than if you got into such a position with your relative(s).

And that (probably) unwritten agreement about giving her house to her caregiver is not a good way for any of this to unfold. Your family is probably coming to the conclusion that the home will be a white elephant and a big tax bill, and not the financial windfall the 'caregiver' was hoping for. Even under the best of financial circumstances, this would be an open-ended agreement with a completely unspecified amount of money. No one wants to feel like they're doing business with such a caregiver, but they are. And this is a lousy way to do business.
* Your mother and your aunt are probably both in a position where they are most vulnerable to scams. If you cannot help out your aunt, at least try to help out your mother to do things like keep strong passwords and set up caller ID on her phone if that's not already done. And that's at an absolute minimum.
* Since all this drama is harming your mother's health, talk to her about maybe seeing her doctor for her stress. There may be meds or even meditation exercises she can do to help herself. I don't know how much you want to run interference, and I don't normally suggest this to people. But if your family is making your mother's life harder, then it may be a good idea to get in between them and tell the family to back off. But keep in mind that may just end up painting a big, fat target on your back.

You're sweet to care. Certainly, your mother and her sister don't deserve this nonsense at this stage in their lives. Your family is not helping one iota. Money and dying/wills and estates are two of the things that cause big fights in families (so are religion, politics, and whether someone is going to have kids).

If I were you, I would do my best to shield my mother and to look at the dealings around my aunt as being almost a dress rehearsal for how they would try to treat my mother. And I would not like what I was seeing, one bit.

Don't let the vultures win.