ALWAYS talk to your neighbors as the very first step when you have a problem. ALWAYS.
Why?
You can't divorce your neighbors.
You are stuck with them, and their dogs, kids, noise, whatever, until you move. Most people don't like moving - this is why and how you get neighbor wars. People don't talk until they are furious and go over ranting and raving and shouting and next thing you know it's the Hatfields and McCoys.
So talk to them because you can't divorce your neighbors. Be a grown-up, use your words and be nice. You can always scream and yell and threaten later, but starting out that way never ends well. So slip on the big-girl-pants, get a nice coffee cake and go over with it and say;
"Hey, we haven't properly met. I'm your neighbor, SilkieKeeper. I don't want to get off on the wrong foot, but it really bothers me when your dog comes into my yard, he makes me nervous and I'd appreciate if you kept him on a lead or in a fence or something."
"Oh, Cujo would never ..."
<smile> "I'm sure he wouldn't, you're probably taking him to the trainer in town <hand over business card of local trainer>, but all the same, I don't like it when he comes by and I'd appreciate if you kept him home. It was a pleasure meeting you!! If you ever need anything, please call <hand over your #>. See you around!"
Takes 5 minutes, and leaves them with a sinking feeling like they're a jerk if they do anything except for what you asked because you are so nice. No one wants to be the bad guy, everyone wants to feel justified in what they do. Think about it - when people shoot dogs, in their mind, they're not the monster that murdered Lassie, they think of themselves as the hero that saved the flock or the vigilante that keeps order, right? When you talk to them, YOU have a chance to write the script.