I know my rights as well. And if your dog is on top of my coop or jumping on the fence or trying to dig under, then I'm allowed (and encouraged by Animal Control/Sheriff's Office) to shoot it. That is the law here in AR. In some states, you have to wait until the dog has a bird in its mouth and is doing harm. In other states, running around and scaring the birds (causing loss of egg production from stress) is enough reason to shoot. Here, looking like the dog that caused a problem last week is probable cause for deadly force.
If you come onto my property, threatening me because I shot your dog, it's pretty darn likely that you will be joining him. And I don't use rocksalt in my guns. That would send me to jail for assault (or animal cruelty). If I have reason to pull a firearm, it's for deadly force only.
ETA: I read the OP as having a coop and run, but sometimes free-ranging. When I free-range, no the yard isn't fenced. Not allowed to do it since we rent. If a dog enters my property, then it's chased off. No reason what-so-ever for a dog to be in my yard. That would be like saying that it's ok for my neighbor's dog to poop in my yard since I don't have a fence.