This is really a tough one.
You are being more patient then I would be. It is a terrible thing you are going through, but just try to remember this thing, The dog is only doing what is his instinct, he does not know any better. Any one with dogs can tell you the dog has to be taught that killing the chickens is wrong, and she is shirking her duties.
You really only have two options here, you cannot just do nothing and rely on her building a better fence, he has killed once he wil do it again.
You can shoot it, and you have that right but you also have to live with yourself. We raise animals for eggs and or their meat not just to slaughter and toss. This dog is also the victim.
I tend to think the second option is best, take it to a shelter and tell them it is either your dog and make up some story why you have to give it up, or say your child is allergic or something, just get it away. If you leave it some place it will only come back. This way you are not left with guilt feelings, and you are a sensitive person or you would have shot it a long time ago, right?