MissFrizz,
All excellent perspectives and suggestions. And one more [I hope].
One issue may be that your Mom implicitly may ask
without saying it, "Whom do you love ["or love more"] -- him, or me?" And/or may feel
without saying it, that, "If you help him, you have taken sides against me." And/or, may feel
without saying it, that, "If you help him, you obviously do not understand or appreciate how much pain he caused me." Or, similar thoughts or feelings that may remain unstated.
In case that may happen when you tell her, it may help if you say right from the beginning, and repeat it, that you love your Mom no less, that you are not minimizing or ignoring her pain caused by your Dad, that you would do the same for her if she needed a kidney, etc. -- without requiring her to verbalize those thoughts first.
Yes, live organ donation can arouse powerful emotions, some surprising because they are so negative. Witness Clark: a dear friend still estranged??
I/we wish you all the best!
Bill