Your example of his reaction to your son falling down doesn't really seem inappropriate or uncaring or bothersome to me. If the kid hurts himself, then yes, caring and comforting is in order. But if he falls down that doesn't necessarily require coddling every single time. Kids fall down a lot. They're also pretty durable.

This example does however highlight that you have very different expectations for how you should treat your children. You're more snuggles and he's more "suck it up". In moderation, neither approach is wrong. But I think your different expectations really color how you're seeing the rest of the story.

I think it's silly that he says being emotional is something "men don't do." However, if HE is not an emotionally expressive person, I think it is unfair to expect him to change his ways.

I also think that it's important to remember that having a sick child, having a sick partner, and being sick yourself are all stressful situations that don't bring out the best in us. It might be helpful to take a step back and talk to a neutral third party about these events to suss out what is the stress talking on your part, and what is the stress talking on his part.

Would you normally take care of the kids unbegrudgingly when they are sick? Are you blowing his actions out of proportion this time now knowing how severe the illness was? Before this incident, were you ok with the division of labor where you do the childcare and he supports your family? Obviously things need to adjust now for your baby's chronic illness, but if things have always been this way, and you were always ok with it, then the stress is probably partially blame for these new objections. I'm not saying they're wrong, or that you shouldn't address them, just that you should think carefully about how you really feel before talking to him.