Please do all of the legal manuevers first - and get her out of the nursing home (if that's really what it is). An attorney may be needed to change the ownership of property back into your mothers control - preferably thru a revocable living trust. In the future, unscrupulous relatives will find it hard to take off with some of her money.
Then, at some point, have her evaluated by a doctor. You very well may need a second doctors opinion to get a release - check with an attorney. If it is the early stages of dementia, it could very well work out fine at your sisters house for a few years.
But, eventually .... it likely would require a 24/7 trained caregiver ...... and then ultimately a Home for dementia (if that's what it is) .... not a nursing home. My Mother spent the last 16-months of her life - until last week - in an Assisted Living Home for Dementia & Parkinsons. It was very specialized. They were exceptionally good - but in time, it can get expensive.
Personally, if there was any way to pressure the people who did this to your Mother - and check with an attorney - but I would consider filing legal charges - or threaten to. It's disgraceful to do that to your Mom.
Peace and wellness
Rob & Gizmo