Follow the advice of the officer and animal control, in that order, if you don't get resolution on the first step. If they're willing to compensate fully, without having to go to the court system, then you're both done, and you can replace your birds right away. If not, then go to the court system, file a civil suit, and ask for WAYYYY more than you'd think, otherwise, because you have to factor in your petting farm receipts, future earnings, the cost of filing the civil suit, the cost of legal representation, if your claims are higher than the small claims court limits are, etc. You can start high, but it's the jurors who decide how much, if you go to a district court rather than small claims and end up in a jury trial. If you don't ask for more, you're going to be shorted, in the long run.
You need to figure the cost of getting new chicks, raising them to the age where they can be introduced into your petting farm, etc., the cost of having to buy eggs to supply for your family for that time of getting the chicks to the age of laying, new fencing and perimeter to keep their dogs out of your property, etc. So, I'd say a minimum of $5,000 in a lawsuit. That would also scare the owners of the dogs into compliance.