Protecting your kids and livestock is not being an "arrogant horse's ass", at least not in my book. You have told them many times already and they obviously did not take you or your concerns seriously.
Some people just don't want or are too lazy to live up to their dog keeper responsibilities...
Maybe not bad, but sure enough more than negligent for a long time.
And even more so knowing that you have small kids that might be endagered by his uncontrolled straying dogs out on another one of their many killing sprees.