Quoting Jas ♥:" She sounds lonely, sad, frustrated and depressed. I'm your sister's age and I have had a 3 year old and ... [snip!] ... to her children. Not your mother. If I was your mom, I'd be having a talk with her and give her a deadline for her to move out."
That was my thought.
OP~ have you thought about your sister possibly suffereing from depression? I love my kids and begged god every night for the chance to become a mother for YEARS. There was a time when I didn't want to attach to the kids. I would wrap myself up in house work or the computer just so that I could have little interaction. Guess what? PPD was my culprit. Since getting that situation back under control I am back to the mom I was and should always be.
She has a lot on her plate. Self induced but it is clearly more than she can handle.