OP - It seems that you have a somewhat good relationship with the kids, so have you considered just telling them not to take your eggs? Explain to them that if they want eggs for eating, you will give them some, but that you don't want your eggs broken or stolen because you use them for food (or hatching). Doesn't mean I wouldn't still put a lock on the chicken coop, but I would still say something (firmly, but nicely) to the kids. They aren't getting guidance at home, but you can set ground rules for how they are expected to act around your house.
I would be really careful where I put electric fencing, since you know that there are kids who could come in contact with it. One poster suggested shooting the kids with paintballs. Really? I'm pretty sure someone would call CPS or the cops on you for that.
I would probably keep a log of everything for awhile (drug activities, kids lack of supervision, etc.) and present it to the proper authorities - not that it will do any good. I remember a suggestion on the other thread regarding a trail cam aimed at the other house to record activity. Not a bad idea.
You might check with your insurance provider on the security system. We found a local security system that charges 1/2 what ADT charges for monitoring, and the discount on our homeowners is almost enough to cover the cost of monitoring. Good Luck!