Raffeer

The only thing I can think of to add to Martha's excellent post is that your family should make sure the ducks lined up in a row include a medical power of attorney, a durable power of attorney and, if she is able to give them, your Grandmother's wishes concerning end stage care.
I suspect the most difficult thing for your Mother will be admitting that she needs help in caring for her Mother. That is a VERY big step. I was lucky enough to have found this site and to have realized that I was not the only one going through this.
My husband is now in a local facility where he is getting far better care than I could ever have given him. I visit for a few minutes everyday so I have a very good idea of what transpires there.
It was only through reading other's experiences that I was able to get past the preconceived ideas so many of us have concerning care outside of the home.
Please have your mother come visit us.
Raffeer