Hi Alice,
It sounds like the culture in your area has some similarities to our area. Thankfully, our neighbors for the most part, are far more courteous than the folks you are dealing with. I had a friend in So. Cal. with a guard dog ridgeback and experienced similar issues with small dogs; except, there they think his dog should be killed for attacking strays in his own yard. At least your neighbors are not that crazy!
I appreciate your defense of your other dog. Laws being different in areas are reflected in both yours and Jay's take. I know here, all dogs are required to have their county tag on at all times (shows owned and rabies shots). Any dog without is assumed wild / feral and possibly rabid. I do feel it wrong that a "pet" dog pays the price for a bad owner; hence, my neighbors pit was given pass after pass. Unfortunately we all have neighbors who are irresponsible; each of us have to decide how much we and our animals under our care are going to suffer as a result. I do not live in a large neighborhood, and, know who owns what dogs...tags or not, come or not they are known to me...first step on any of them would be to get them back to their owner and resolve any poultry damage (they try to take down my goats or Alpacas, no pass). The neighborhood 6 miles away has dogs get loose from time to time and they tend to come our way; those I look for a tag and call to me; even a very scared (peeing on herself) medium dog came to me. While she was dirty from running, you could see she was a pet; she also was not after my animals...just lost and scared. In each case, I got the pet back to the caring owners. I did let each know that we and several neighbors have livestock and it would not be safe for their pet to get out again. To date, we have not had to shoot any ferals. We have had to deal with foxes and cats.
I appreciate your ideas on no kill options. I do think they are very valid for casual trespassers. However, the pit we had an issue with was hunting and devouring poultry (ours and others). (The owner believes he should only feed his dog when she does not find enough food.) Animals hunting their food source do not scare away... they just try to hunt more stealthy. Upon acquiring the additional livestock, we needed to be able to immediately stop any attack on them as they are not so easily replaced.
The type of property perimeter that would prevent all problems is not feasible. We are also in a culture that believes fences are "rude". Prior to moving in, the guy two parcels down had to apologies for putting up a fencing on a third of his property that was where other neighbors could see! (He had bought 3 horses and needed it for them! BTW we are all on Ag land). We have gotten a lot of negative feedback about enclosing a front / back yard area (no view of it for anyone...and it is picketed) and for enclosing the paddock field and barn (also no view issue) with wooden horse / livestock fencing! I do not understand this as I am very accustom to fences. I could understand a dislike for cheap metal or chainlink fencing that is in plain view on the edges of our forests, but being upset over quality fencing hidden on our interior? Hence, between the cost and the backlash we just do not see any permanent containment structure for our acreage perimeter an option. We will be planting lots of wild blackberries on the edges to feed the critters and encourage all animals to stay on the outside...a live fence will help a lot! It does take time to establish though.