Whoa, so this isn't some kind of hypothetical situation, eh?
I guess, if I were you, I would do research on the kinds of diseases that can cause kidney damage, and see if any of my family were at risk for them first. If so, I'd hold onto the kidney. If everyone is kidney-healthy, then I would look to the reason why her's are failing--something hereditary, or habitual? If it's habitual and she is likely to ruin the new kidney like she did the old, then there's not much point. If it's not habitual, then yes, I would probably donate the kidney, for her kids. Even an abusive mom is hard to lose.
There's something else to consider too. If she might die without a transplant, could you sleep well at night, knowing you could have saved her? Even if she was a real monster, I don't think my conscience would be free from that no matter how much I tried to reason with it. Knowing you could have stopped something bad but you didn't is the sort of thing that can haunt a person.
Dat's my take on it. Hope everything goes well for you and her, regardless of what you choose to do.