My home, with a strange mix of cats, dog, rodents, snakes, chickens.......anyway, it is a constant juggling act to make sure no one gets killed. I can't iamgine killing an animal you CHOSE to have for doing what came natural. Obviously you will do what you see fit and I am sure the poor dog will be on the losing end. When will people learn there are other more humane, more logical, ways.
Edit to say, the more I think about this the more upset I feel. Yeah, it is actually disturbing my sleep. When I take my kids to school I make sure their tummies are full, their clothes are comfortable, and they are happy and ready to start their day. I try to make sure nothing upsetting happens before they leave for the day. I have found a pet dead and didn't tell them until that evening so they wouldn't go to school sad. I can't even imagine letting my kids spend the entire day upset and worried, knowing their father is killing their dog sometime while they are gone. That is a special breed of cruelty in my opinion.