I am new to this forum, but wanted to jump in with my own observations.
This dog has bitten not once, but twice, and, the second bite was more severe than the first. Fortunately, neither bite was catastrophic. The next one very well may be catastrophic especially if the dog continues the pattern of biting children. As much as I hate it, I agree that the best route here is a calm and peaceful goodbye at the vet's office.
Even if you were to find the right home, with no children or pets, chances are that you are not going to find a family that is experienced enough to handle a "biter" and that endangers this dog, as well as countless other people.
Baby gates, outside kennels may seem appropriate from an emotional state, but baby gates fall and children open gates. If the dog is not safe to have around the children while you are supervising, the dog is just not safe to have around any children.
It is not fair to cage the dog up and separate him from his family........it could possibly make things worse and cause a higher level of aggression, imo. It's not fair to the child to have areas of his own home that are not safe for him to be in, and it's not fair for mom and dad to have to deal with that kind of worry all the time. Euthanasia is rough for any reason, but to have to put down a healthy dog just is rotten. I have had to do it, and it REALLY is awful. But, sometimes it is the most fair thing to do, for everyone involved.
I am so sorry that you are having to make such a decision. My heart goes out to you no matter what you decide.