Oh yeah...on topic.....

I think this boils down to respect. Your neighbor believes you (your kids) are showing him a lack of respect for making what he considers to be excessive noise. He therefore returns the perceived disrespect by showing you the same lack of respect. I think that the HOA and police are only going to make things worse. He may stop after being admonished by one or the other (or both) but the seed of anger will likely only germinate and sprout stronger than ever (hopefully still non-violently).

The only way to fix this is to restore the sense of respect on both sides of the wall. Sure, it's easier said than done but once accomplished, it'll have longer lasting effects, and positive ones at that. Perhaps a 6-pack of whatever on his porch with a note requesting a conversation at a neutral location so you can try to work through it will get the ball rolling.