The thing about your post that got my attention is that a sick kid is going through pure hell inside as it is with all the stress and worries that goes with an illness. Not to mention that a kid doesn't even have adult skills to help them handle stress properly.

So, family drama is just liable to give this yougen a nervous breakdown.
My point is try talking to her from that perspective. Tell her, it isn't about you and her, just the kid you want to have as much inner peace as he can no matter what it takes from either of you.