If you view my profile pic you will see my Miata, and in the passenger's seat my son Will (when he was much younger). Yesterday was Will's first track day -- although he had done some parade laps in the past. He used that same Miata, on the same course). He did spectacularly well -- I was his instructor for the first session (his choice, not mine), and I realized I just needed to be quiet and let him drive. His thousands of track laps as a passenger at HPDE events have clearly taught him valuable skills .
He scared me once. But, if you have instructed, you know that you can be scared by competence, as well as incompetence. Will took a sweeping right at the end of the straight with far more speed and aggression than I had anticipated. And he did it well within his skill set. I was, and am, very, very proud of his driving.
The take away? Bring your kids to the track when you go. Let your track friends be mentors. Get your kids in the passenger seat as soon as you can.
Hannah, my daughter, watched from the grandstands -- and she is already scheming to get her hands on my M3 when she is old enough to participate.