I get no help from anyone. Any advice?

I know the way your sister is acting isn’t fair. It’s aggravating and you are stressed out. Maybe it’s because I am an only child, but I learned early on to be self-sufficient and not count on anyone but myself. I am my husband’s sole caregiver. He is bedridden and I do everything but feed him. I have two children who don’t even ask how their father is. I understand they have lives and families of their own, I know they’d be there (and have been) in an emergency, but it’s only me in the trenches.

From my perspective on your situation, you really need to let go of this anger at your sister. She’s not bothered at all by it, and it’s eating you up. As far as being there to beg money from Mom, well, it didn’t come out of YOUR pocket. She’s the one who has to live with that. It may have been an emergency situation for her and the only one she could turn to was Mom. When sister makes comments, smile and say “Thank you for your input. I’ll take it under consideration!”

See if you can ramp up the respite care. Even to the point of inquiring at your church if they have volunteers who might provide an hour visit here and there. And, there’s always placement in a facility.

When I made the choice to become a caregiver I did it with the full knowledge that it was MY choice and with no expectation that my sib would be part of the care plan, in fact she told me many times that she couldn't do what I was doing. Yes, I griped that she could have been more involved but that was really just cursing the fates, I knew that it just wasn't part of the plan. It sounds as though it is time for you to reevaluate what you are doing, you need to realistically look at how what you are doing is working for you and how to make changes if it is not. Hire outside caregivers? Regularly scheduled respite? A plan B when it all becomes too much? And don't totally discount the things your sister is telling you, her perspective may be different than yours but that doesn't mean it is wrong.

I've been exactly where you are. Trust me when I say you cannot guilt someone into caring if they don't already. Your sister knows you'll continue doing everything without her needing to lift a hand and that's probably good enough for her.

There are natural nurturers and then there are people like your
sister, my sister. Like a lot of
people's sisters and brothers etc.
If she thinks she is qualified to give you advice based on nothing she sounds like a pain and I doubt nothing you could say will change that.

Whose decision was it to have your Mum move in with you, or did you move in with her?

Was it your choice? Was your sister consulted? Was there an agreement in place that she would relieve you on a regular basis? What alternatives are available for your mother's care?