IANAL, but...

There are some factors at play or more but I think this is gonna be a tough one for you.

• A dog owner is responsible for maintaining control over their dogs at all times
• A home owner can protect his home with as much force as is required but not with excessive force
• A gun owner must use guns only as a last resort when their lives are threatened and only to stop the threat against their lives
• Hearsay is inadmissible
• Were there NO TRESPASSING signs posted?
• Have you had any other possible history with this neighbor?
• Is your deceased dog a breed normally associated with violence?
• Were the crops in at the time of the shooting? Is this a cash crop or is his field for hay? I can see he has tended to the land for farming... so this could fall under some strange regulation about farmers using firearms to protect their fields or seed... but you should have your lawyer dig into it a little before you decide to proceed that way.

From the diagram you posted, the shooter could possibly claim his life was being threatened if the dog was rushing towards him. This map could work against you in court but I suppose the truth is what matters so you should simply state the facts and then maybe you will feel better about this a little, although I know it must be very hard for you to do so. Losing a dog is like losing a family member.

The thing is though this guy was armed at night and possibly laying in wait. That's something you should explore. Why was he there? Is that legal in your state for someone to "guard" a field with a firearm and attempt to use deadly force?

3-4 shots could be considered excessive, unless he missed a few times and the dog was still rushing towards him before getting hit. The fact your dog made it back indicates some of those shots were misses.

What were his motives being armed? It seems as though there aren't any structures where he was so then you have to assume he was waiting for someone or some animal to cross into his field.

At the end of the day, every pet owner must keep their pet leashed at all times when not in a pet-proof fenced area or in their home. You're responsible to keep your pet safe. Don't let your other dog off leash unless you have constructed a safe run area on your property so go buy some thick coup wire and construct something he can't dig under. Dig the fence deep into the earth and put a several feet depth of pea gravel all around the perimeter so he can't get loose easily and use cement pilings for the fence.

Protect your family by keeping them on your property WHILE you see if you can get some justice for your dog... but you might end up wasting a lot of money going after this guy if the case is thin.