My opinion ... and it may sound strong, but you asked ... you should not watch him.  You know best how your child responds to illness and it sounds like it can be a challenge.  No matter how much you try to shield your child from illness, they will get sick anyway at some point and build all the necessary immunities.  That’s life and that’s ok.  So why would you choose to increase their risk of getting sick by watching someone else’s sick child?  Your primary responsibility is to protect and care for your child.  Your sister-in-law must do the same with hers.  Of course you try and help when you can for the love of the kids, but not at the expense of your own child.  And if your nephew is sick often, you would be better to address this from the get go or you’ll be facing the same issue week and week.  That’s too stressful.  I don’t mean to sound unkind or insensitive.  My husband says I’m a "sap" and go way out of my way to help other people’s kids, cause I love kids.  But at some point you have to draw the line to protect your own and there’s nothing wrong with that.  It really doesn’t matter whether others understand or not.  They don’t live with the consequences ... you do.    Hope that helps.

M