Dog "biting" kids… 9 times out of 10, the kids started it and the dog gave ample warning. Our Rocky grabbed our daughter's hand once when she starting playing with him too rough while he was trying to nap. He low rumbled (we told her to stop, Rocky not like that), then he low growled (stop, Rocky getting mad), then he just grabed her hand. Didn't break the skin but it was quick and for her, just the reprimand she needed. She was startled, not hurt, and she has never done it again.
I'm not advocating teaching your dog to be agreesive with children or anyone else who walks in your door. The dogs view your kids like pups and discipline them as such.
And for those out there who think I'm a horrible mom now, my husband or I are always around when the kids and dogs are together and we keep a very close eye on their interactions. If any of them start to step out of line or beyond the boundaries of politeness, the offender gets a time out to decompress and calm down. Both kids and dogs need to learn their boundaries. I often say I don't have two kids, I actually have four or five (but only two ahve two legs, the rest all walk on four!)