I have tried multiple times to stop my sister from feeding into and encouraging my mother to be hateful to me. She feeds into my mother’s dementia in accusation of theft. I’m at a point of turning off the phone so she cannot talk to her because it causes so much trouble for me.
At 90 years old, living alone and easily manipulated means that she is vulnerable. APS will go check on her and get the proper agencies involved to get her the help she needs.
Let her make the accusations, they will check everything out and clear your name of wrongdoing. This is far better than living with the constant threats. Bring it on and be done with it.
Please do not block your sister. There are issues with isolation and cutting contact that scream of abuse, even when it is not there, these actions make it look likely.
Let mom and sister figure out how to get the groceries. While you are waiting for APS to respond to your call of a vulnerable senior.