I'd like to weigh in, if you don't mind. I took Merlin to Petco classes, but I think my input is probably still applicable.
First, I think that training classes are great. Your dog gets exposure to other dogs in a more controlled environment.
Second, if you are wanting your kids to learn to work with your dog as well as you, it might be beneficial to seek out a trainer and do some individual sessions, or find a group class that will be small enough that you guys can get some individual time with the trainer. I found that to be an issue in my first class simply because there were quite a few of us and only one trainer.
Thirdly, keep training with your pup until you find a class. I was extremely happy that I had taught Merlin certain cues already before I went to the class. It helps build a base line for behavior, but it also strenghtens your bond before you start the class.
Anyway, that's my input. Be sure to look for a positive reinforcement trainer that doesn't use aversive techniques or aversive equipment (choke chains, prong collars, etc.)