I would post no trespassing signs, and then use your local law enforcement, documentation is everything here, take pics of dmg, take pics of the kids in the property, and pursue legal charges.
This is probably your best route. As much fun as it would be to tar, feather, paint, zap, etc. these kids you would be setting yourself up for a nasty lawsuit if they were injured.
What's really sad is that in this town the cops won't be bothered to come to a car accident scene if an ambulance is not needed so no way are they going to respond to calls of kids in someone's yard...but I bet if I haul off and slap the spit out of one of them the SWAT team would probably show up in no time flat.
Seems like NO TRESPASSING signs would be the obvious first step, if only to protect yourself from liability if they injury themselves in your yard when not welcomed. Think about calling CPS? If the house is as dysfunctional as you say, CPS might find them a new home...