As a former campground host in a forest service campground built by the CCC, I would suggest that the best time to camp if you are seeking quiet would be mid-week, when the folks with small kids are all at work and the campgrounds are mostly deserted. And if you want real peace and quiet, boon docking is your ticket. If there's nobody around, their kids won't be there either.
For what it's worth, the only time I had trouble with screaming kids in the 5 years I did the hosting thing, a couple with 3 kids were completely unable to control the little hellions at 11 PM. Multiple requests to keep it down went unheeded until I had to threaten them with eviction from the park. "But we'd be just as noisy packing up . . . ." No, you don't get it; if I have to evict you, it means leave your stuff and get out, you can return to pick it up in the morning, and I'll get law enforcement to help you leave if it comes to that.
Ah, but I digress. During the day, in a busy/crowded and popular recreation area, kids noises will abound. See above for the only way I know of to avoid that.