Picture your kids at the wheel of a car, accelerating down a straightaway—70, 80, 90 miles per hour. There's a big curve up ahead. Yo'‚re in another car, giving chase. A parent's nightmare? A dazzling new video game? No way. Zipped into brightly colored Nomex flame-retardant racing suits, wearing crash helmets ("lids," the pros call them) and strapped into the open cockpits of four classically shaped race cars, my son, two daughters, and I roar around Lime Rock Park on a heart-thumping, pulse-elevating experience, negotiating the 1.53-mile track's twists and turns—acing the 180-degree double apex right turn called Big Bend, maneuvering through the taxing Esses, the Left Hander and the Right Hander, all the while learning some valuable lessons about road dynamics and the safe handling of a motor vehicle under challenging circumstances that could be put to use in the real world.

I'd signed us up for what the Skip Barber Racing School benignly calls Introduction to Racing. That‚s like describing a hot-fudge sundae as nothing more than a bowl of ice cream. Let me put it another way: The time we spent behind the wheel of the 150-horsepower, two-liter, four-cylinder, 1,150-pound chariots of fun was like having our own reality show—our family's version of The Amazing Race.

The experience had begun to take shape months before, during a holiday party, when I instructed my offspring to close their eyes and open their hands. Adam, Sarah, and Jennie, all in their thirties, surprisingly obeyed. I placed a bright-green lime in their one hand. A rock in the other. Jennie was the first to catch on. "Lime Rock!" she shouted. "We're going racing at Lime Rock? Awesome!"

Awesome proved to be an understatement. The weather that June morning was Litchfield County perfect. The 300-acre park—or half a century the scene of many epic contests of skill, courage, and endurance—was capped by a sun-filled sky that splashed the surrounding green wreath of the Berkshire Mountains with light. The track was dry and fast, just the way the pros like it. And hey, if it were good enough for them, it was better than okay for a family of racing rookies who could pluck down about $600 per head to satisfy their spirit of competition and a passion for going outside the lines of the ordinary.

Any trepidation that squeezed our gut—we spotted two damaged racecars off to the side near where we parked—quickly dissolved after we trooped into a small meeting room for the pre-lim: a chalkboard tutorial acquainting us with the characteristics of the track and the peculiarities of the cars we'd be piloting. It included instruction on how to down-shift, how to corner, when to brake and accelerate, how to prevent a skid, how to avoid crashing into one another. Sure, we were told, the idea was to have fun, but the emphasis was on safety. Recklessness would not be tolerated—imagine driving without a cell phone glued to your ear.