I would not kill my dogs either, my dogs protect my grandkids, they protect me there is NO doubt if someone was going to hurt a family member my dogs would rip the throut out of the person trying to hurt us. Yet my youngest grandchild can climb all over the dogs and the dogs worship the ground all the kids walk on.
My dogs are big house dogs and I know if my chickens get out my female dog would play with it to the death. I would blame me like you blame yourself but no way would I harm one of my dogs.
I'm fortunate that I have a large fenced in area for the dogs and away from them a large fenced covered area for my chickens.