If someone came onto your property and hacked down tree branches, that would be considered vandalism, because it would technically be destroying your property. The point is that if branches hang over, they technically are not on your property anymore.

"What type of doggie to you have? I believe that a dogs bark is a blessing! It lets you know something is lurking. "

Yes, a CONTROLLED bark is a blessing. According to the story, kids were walking by, the dogs (who were in the house) started barking and growling at them, so, the kids hit the fence. You cannot blame children for walking by your house on a public walk, so, to prevent the issue at the root, you train your dogs to stop barking when you tell them to. This whole issue probably could have been avoided with some simple training.
Our pups are mixies. English bulldog, American bulldog, cockerspaniel and presumably fox terrier. The one girl looks mostly like a bulldog/boxer, the other girl looks like the designer mutt "beabull" (mix between a beagle and an American bulldog). Our pups were trained with commands and praise, not with tools that prevent barking with pain or shock. If they feel they need to, they do bark (ie, Bailey will bark once when someone is at the door, exactly one time, no more than that) but they're not obsessive, and they know when it's ok to bark and how much. I don't allow them to bark and try to attack anybody that walks by, but, yes, they can bark if necessary, and do bark on occasion when they're playing with each other. It's all about teaching your dog boundries (I guess people have to have boundries before they teach their pets boundries though), and how to behave.

Anyways, as I've said before, I think it's wrong to teach a dog that it's ok to "attack" anybody that walks by and touches "your" branches. I also think it's unbelievably wrong to verbally and physically attack children (if they're under 18, they're children, no matter if they're some 400 pound obese child, a 200lb football player or a 4' little shrimp of a child). It could and should have been prevented with simple training and possibly anger management. They're KIDS, they do goof around, and I very highly doubt that kids walking to a field trip were planning on breaking into your house, molesting your little sister or attacking you. Either way, we disagree, can we agree to disagree? If not, well, this discussion could go on for the next ten years if we really felt like it, but, honestly, it's not doing much of anything except wasting time, IMO, as we've gotten our points out and we're obviously never going to agree.