I'd have a chat with kids prior to arrival to try to get them on best possible behavior-at least fairly quiet and not out running around at night. At the site if no one is causing a ruckus I doubt they're counting too carefully. I haven't recently camped at Yellowstone but in other National Parks (Zion) they also have quite a few people permitted per campsite, and we often have dinner at one site with ten people or more (we have two or three sites but all get together). No one has ever said anything about that.
At Zion I do pull up to a ranger office to check in and I suppose they could count bodies at that time if I was in a truck.
A little extra donation would be great...
