My 2 cents for what it's worth.
I would ask the parents to reimburse you for the financial cost of your loss. If they do not, then I would take the parents to small claims court for the cost of the dead birds, the cost of the cleanup (there is now biohazardous waste rotting in your garage which may require professional clean-up if their rotting bodies begin to seep into the concrete before you get home). Do you have COPIES of the instructions you left? Those will come in REAL handy in small claims court. You may prefer to not have discord with your neighbors, but it's not like YOU created the discord. Also, if you take them to court, include not only the cost of said dead birds and clean-up but also whatever it will cost you in additional expenses, shipping, etc., to get new ones, AS WELL AS the cost of whatever cage or container they were in that is no longer usable because of the biohazardous waste.
It's not about getting revenge on your neighbors. It's business, plain and simple. It's about recuping the costs lost by their negligence, and you would not be outside the realm of what is right to request that from your neighbors, whom you PAID to follow your instructions.
Regardless of the age of the kid(s) you left in charge, the parents are ultimately responsible for what their kids do or don't do, especially if they "verified" that the instructions were followed. Obviously, their verification process is pretty lacking.
Somebody's been smokin' the hay or something over there.