No more warning shots. These dogs won't stop attacking you and your dog. If they get to your children they'll attack your children too.
They've been *trained* to be fighting dogs / attack dogs. See, by NOT training a dog, we still train behaviors into them. By allowing aggression, we're training them to be aggressive. These dogs never had a job or found their proper rank in their "pack". I've met a lot of poorly trained or semi aggressive dogs who HAVE been retrained into fantastic and safe animals. But I've never met an attack dog or prof. fighting dogs to recover. They'll go for blood. Every time. It's wired into them.
How do you move on? The dogs die. I hate it too and it's not fair because it's not the dogs fault. But the dogs are not going to just one day up and change. Not even with the most strict training program. It's a done deal. Your neighbors screwed up those dogs to the point where your life, and your children's, is at risk. That's serious. You're afraid because you should be afraid, yah know?
I really, really hope the owners don't re-home these dogs. Because they are dangerous now. Permanently. To hand them off would be potentially devastating because their next owners won't be ready when suddenly the dogs are going after their kids. They won't be prepared.
Do what you need to and make sure those dogs are put out of their misery (a dog without a job is an unhappy job - a dog desires to know it's place and duty). Your not doing anyone a favor by keeping them alive. Someone is going to get very, very badly hurt by them if they are not put down.
Good luck and big hugs.