No you are not being unreasonable, I would feel the same. And I know my fiance would probably have done the same thing as your husband, giving the same reasons and looking at me like I was the most awkward, uncaring person to let my emetophobia interfere with looking after a sick child. The thing is they just don't understand how we feel as they don't suffer from it.
Last year, we were waiting for my fiance's seven year old daughter to be dropped off by her mum at our home as she was coming up to stay with us for a week or so. They were running late, then we got a phone call from his daughter to say she had v*ed during the journey and that's why they were running late. She never gets travel sick so alarm bells started ringing. When she arrived she had messy clothes from the v* and announced that she also had diarrhoea, and had done for the last two days. I was so scared (and angry her mother hadbrought herup when she was obviously suffering badly with diarrohea and sickness), but my fiance just got irritated with me and gave me the silent treatment. She was quite bad all week with diarrhoea, my fiance had to take her to see his doctor, but as luck would have it didn't v* whilst she was with us. It was one hell of a week though, and I was convinced I would catch the stomach bug she had (especially since she's a very cuddly girl and is always snuggling up to you and kissing you, bless her). I survived though!
Anyway, hope you and your family manage to avoid what your nephew has.
.•:*¨¨*:•.Tracey.•:*¨¨*:•.
Fall seven times, stand up eight.
- Japanese proverb