I think your neighbors are totally out of line to let their dogs run free. However, I can't blame someone for avoiding talking to you and not apologizing to you after your husband's reaction was to threaten shooting--not something more normal like reporting them but, shooting them.
That was my first thought too.
While I would typically be over the top apologetic, I might avoid somebody who seemed crazy and was threatening shooting. And while threatening to shoot a dog that kills livestock may be normal in some parts, it does put the owner on the defensive, almost guaranteeing you won't be getting an apology.
I have had livestock. At least where I lived, it was always the owner's absolute responsibility to keep their livestock safe. If it wasn't the neighbor's dog, there was always the wild dogs, the coyotes, the foxes, the birds of prey. She even says that it would be an ok oops if it was a natural predator. Well, dogs are natural predators. Yes, dogs should be contained, but people are stupid and let their dogs roam free.
While I think the neighbor was way, way over the line and at fault, I also think the OP is also over the line and shares in some responsibility for not keeping the chickens safe from predators, be it the neighbor's dog or the fox in that open field next door.
Just report the dogs and keep your chickens behind a fence where predators can't get to them.
And for the record, you can't compare a dog killing a chicken to a dog coming onto somebody's property and biting a child. Chickens are normal to some breeds, biting people is not for any breed.