One of the biggest complaints I hear from campground managers is that some parests use ATVs as babysitters.  And having stayed in Campgrounds back east that allow this practice, let me give you an example.  All day long three kids rode round and round the campground on a small ATV, but noisey.  All three at the same time, no helmets and round and round the same circle all day long.  We knew that after dark they'd have to stop as the ATV had no lights on it.  Well at dark they stopped for about five minutes, then a slightly older child started riding another ATV behind them with its lights on.  And around and round they went, till just before midnight when the little ATV turned over spilling the three small children onto the pavement.  And they were promptly run over by the other following ATV with its lights on.  It turns out that the parents were still out riding their ATVs on a night ride on the trail.
Well when they got back they found that their children had been taken by ambulance to a hopital thirty miles away.  Two of them were DOA and the other became paralyzed for the rest of her life.  The older brother who ran over them has been in and out of mental institutions since then.  

All that being said, I salute you for taking the time to train your children and looking for a proper place to do it.  As we all know ATVs are not babysitters.  Another fatality that I've seen just after it happened was a nine year old weighing all of 70lbs trying to climb a steep hill on a Polaris 500, the bike went over on top of him.  The parents were found later drinking beer and skinny dipping in the river.

We must train our children well, keep them on ATVs that they can handle, and most of all, never leave them unsuppervised.