What were her living arrangement before that?
The clarification is this. Bad, bad idea. Once the roommate moves in there is no piece of paper in the world that will guarantee the roommate's compliance with the rules. Once the problems start you will have a b-tch of a time getting the roommate out and your mother will be stuck paying for a two bedroom apartment.
I suggest you abandon the roommate idea. It's a recipe for disaster. Hell, if it was me I wouldn't want a stranger living in my house with me. I'm 72 and the idea gives me the heebie jeebies.
By the way, no landlord in his right mind would get involved in this other than to have both parties sign the lease jointly and not care what arrangement they made between them.
An alternative would be to find her a one bedroom apartment near you so you can help out. And if she can't get around because of her back, well, there are plenty of stores that can deliver groceries and whatever, as well as things that can be ordered on line for delivery. She can also hire bonded cleaning companies to come in and clean for her. There are so many ways of handling this, without a roommate, so that she is still independent.

