I would sincerely hope that child labor laws make some sort of exception for family businesses.
That being said, Friday and Saturday nights are going to be a pizzeria's busiest time. With that much going on, adult supervision could easily fall by the wayside. If that were to happen, then I definitely don't think an 8 year old in a hectic, unsupervised environment where beer and wine are being consumed is a good idea.
I'm all for passing the torch to future generations, but couldn't the kids learn just as much on a less busy night?