To answer your question, I have never had a dog that is afraid of children. Or should I say, I never would have a dog in my home that was afraid of children.
Sure, a child can kill a dog. Mind you, they'd have to be one seriously mentally disturbed child to do so, and I guess it would also depend on the breed of the dog as to whether a child could kill it.
But a dog can kill a child in a split second. I understand your reason for muzzling Doug. Unfortunately, it's a catch-22 situation, because muzzling him only making it worse for Doug IMHO.
So your little baby is not having this problem with Doug? It's just the other son? Has Doug seen any other children since coming to your home, other than your own?
I am so glad to see how seriously you are treating this dilemma.