I disagree with @jagger on this one. It doesn't seem like its the family's noise that's the issue, more the child egging the dog on. There is definitely things I expect of my neighbors, not barking or yelling at my dog is definitely one of them. Hopefully they catch the child doing it and can curb that behavior, and I'd just continue calmly and consistently letting them know that her barking will settle down, but not until the child lets her be.