For discussion's sake:

There seems to be disparity across regions and states regarding the exact definition of "needed shootin". The west and the south seem to come down on the side of defending the castle at all costs, with liability assumed by the trespasser. The northeast and midwest seem to divide liability between the defender and the aggressor, permitting escalation of defensive response in response to the level of offensive threat. I believe that I have heard of trespassers suing homeowners for excessive response. Chickens are probably property/livestock. Dogs are probably family/fur babies, particularly those wearing clothing. It would be easier to defend killing a dog that was attacking a person than killing one that was destroying property.
Disclaimer: Do not rely on nursing advice offered by a lawyer: do not rely on legal conjecture offered by a nurse, particularly from one whose avatar is a dog.