Pp here--also, my grandmother could put herself together very well for strangers. Only after you sat with her for several hours did you realize just how batty she was. A doctor could come in and she would look and sound totally normal/sane. We had to start taping the crazy stuff to get her diagnosed. So it may be much worse for your sister than you know from an occasional phone call. Go out and spend a week with her 24/7 and then see what you think.

And are you basing this on your mom telling you this stuff? Because I wouldn't believe a word of that if she has a dementia diagnosis. My grandmother had dementia and the last thing she ever said to me was accusing me of trying to kill her. When she wasn't talking to the dead people floating on the ceiling. Approach with caution, many people with dementia become paranoid because they don't understand what is happening to them. It is very sad but not real.

Call the Elder Services or Social Services in your Mother's town and get a case worker. You also need to fly out (unannounced so get a hotel room) and if the sister won't allow you to see your mom then call the police and don't leave until they get there.

You sound like the crazy one, OP.

WTF OP. I would call 911 NOW and get on the next damned plane out there. You are sounding as crazy as your sister.

Get out there, figure out what's happening, hire a lawyer, call the cops and adult protective services. As PPs have said, that's the only thing to do. That and get some help for yourself too once you're home, you don't sound all too stable or rational either.