Sounds like your neighbor and mine should get together and live somewhere AWAY from us chicken owners!
We lost our best and favorite hen this week to my idiot neighbor's dogs that get out on a regular basis. I called the police, they referred to animal control, who came over, took statements from me and the neighbor I get along with, and got copies of the photos I took of the dog on my property, the dead hen, and the one dog on my property eating my hen's head. They issued idiot neighbor a citation and she said she'd fight it. They said good luck on this one. A) the citation is not because the dog ate my hen. It's because the dogs were not on a leash and was on my property, and I have photographic proof of that. The fact that they killed a hen in the process just makes it worse for her in court. Add to that the two years of complaints where they've had dogs running loose that weren't licensed, that have bitten people and attacked cats and wrecked havoc, the animal control officer had to laugh at her.
I live in Ohio, and I told the animal control officer when he said he couldn't take her dogs that day, that I would be forced next time to defend my property under my homeowner's rights. I told him she needed to know as a former Marine, I wasn't going to miss. He said simply to call the sheriff if I had to shoot one of her dogs, just so the report would be filed that I was defending my animals. I went to buy a shotgun and my husband got concerned that the spray would hit one of our dogs or cats or kids or other chickens, so he recommended a BB/Pellet gun. I bought that and spent the day practicing in view of idiot neighbor. Her dogs haven't been outside since, until this morning.
I also got 3 roosters that I'm working into the flock now too. One is a very fast, very spirited bantam that I think should teach those dogs that dynamite comes in small packages.
And for what it's worth: I'm STILL an excellent shot. They should be thankful my husband nixed the shotgun.
I say for you, file a report, photograph or video every instance of their dogs being loose and call the police every time they come after your hens. And don't be afraid to shoot an animal that is okay attacking your hens.