Seems like most of the posters think biting a child is "natural, animal behavior." My vet does not hold with this attitude. We had a really cute, funny rat terrier that we were all in love with. We got him when he was about 10 weeks old, from a friend who couldn't care for him. After a while, it became apparent that he was gonna be a "one-boy" dog, and liked my oldest son the best. At first, he didn't act aggressively towards the other children, just preferred to sleep/play with my oldest.
When he was about 6 mos. old, he bit my son for the first time. Very small bite, did not break the skin, no big deal we thought. If he really meant to harm him, he would have broken the skin, right? This was our thinking at the time, we did our best to watch over him and remove him from the situation if he seemed to be getting hyper. Then, we left him with my MIL when we went on vacation. We returned to find her with a huge bruise on her thigh, when I asked about it, she laughed and said Oreo bit her when she picked up the neighbor's baby. Again, everybody said "oh, that's just the way animals act sometimes, if he really wanted to hurt you he could have."
I called the vet, to ask what kind of behavioral modification training we could do. To my horror, he advised that we put him down. The whole household starting crying, but the vet insisted this was not a situation we could ignore, and that if a dog starts biting, they must not be given to another family. I begged the vet for another solution, and he grudgingly agreed that if we were very, very careful we could try to watch for the danger signs.
For a year, we watched over this dog, removing him if he seemed to be about to bite. Finally, when he was about 3 yrs. old, my oldest came in and asked "where are the Band-Aids?" I told him where they were, then it sank in "why do they need a Band-Aid?" Although they tried to hide it from me, Oreo had bitten my younger son so hard that he almost tore off his left nipple. Out of nowhere, he launched at my son and bit him. I contacted the vet, and he stated that there was nothing else but to put him down. He stated that it was an especially dangerous sign that the bites got worse over time, and that the dog used a tearing motion when he bit my son. My vet stated that there is no behavioral modification for biting, and that we would have to keep him in quarantine for 10 days to watch for rabies, even though we were current with our shots.
This was the hardest thing I've ever had to do. Do I feel guilty, of course I do. But while my dog was being held in quarantine, I would go visit him so he wouldn't be lonely. During one of my visits, an assistant at the vet's office saw my dejected attitude, and said "I'm so glad you're doing the right thing. I didn't, couldn't put my dog down, and she bit my daughter in the face and left scars."
You have to do what is best for your children. We have two Cavalier King Charles Spaniels now, and they are beloved members of our family. After the horrible incident I've described, I searched the internet to find the right breed for our situation, so that this would never happen again.
Good luck, I know it is very hard.