I am just so glad the child was not hurt. We often see kids walking dogs that they can not control because the child is too little. In this case the child and dog might have been fine but for the OP's dog attacking. As an adult, I might have trouble controlling my dog if it was attacked so the fact that it was a child walking the other dog has no bearing on the fact that her dog was attacked. Dog owners are 100% responsible for their dogs at all times. If this child had gotten hurt the responsibility would have been with the OP.