I was not expecting Washizu to offer up his blood like that, but truthfully they were on uneven playing fields even before that with Akagi refusing transfusions
In the past few years, I've picked riichi mahjong so I came back to read this again, and you're right. The doctor might've put it bluntly, but it's insane to entrust a small child with an unemployed man who gambles for his income. I think people just like rooting for the underdog, completely...
I'm guessing Momoka may have been involved in an affair situation before whether it was her being the other woman knowingly or unknowingly or it was her cheating on her partner, but I'm betting it has nothing to do with Rei.