I think that most donors resolve the "what if" issue with that the reality is here and now. What happens in the future is out of our hands. If gd forbid your child needs a kidney in the future you may not even be healthy enough (or alive) to give that gift. So should you hold onto an organ that may be needed versus one that is needed now?
I had an answer like that for a friend who counseled me against donating at first. He reminded me that my kids might one day need organs. I pointed out that none of them was showing any signs of illness and someone "hoarding blessings" wasn't the way I wanted to view myself.
If I worry now about how I might need "it" (for any type of "it") in some uncertain future, then I'd never be able to give so much as a dollar to someone in need, since
someday I might need it.
Her concerns are real and probably feel even more real & immediate to her. Bad Things do happen in people's lives. Are you comfortable facing that future none of us would want, one where you have a bad donation experience, or one where she or your child
does need a kidney later? Maybe if you show that you are taking her concern seriously by accepting these are real possibilities and talking through it with her, that will be a chance for her to talk through your concerns for your family member with you. I'm not saying you haven't talked it through like that, just wondering if she feels heard. A big part of her future hopes and dreams involves a healthy you.
Best of luck to you both.