Took my son last year (he was 12). We weren't planning on Whitney, but after we had some problems (route finding - my fault) on another trip in the area, we headed to Lone Pine and easily snagged an overnight permit. He had Cloud's Rest and multiple San J hikes under his belt that summer, but nothing at altitude. We spent the night at Outpost since I didn't see the need to carry the gear any farther up the trail. He had slept in the cab of my truck the night before at the portal while waiting for our other hike, so he far from rested. We got in the tent around 6:30 pm and he slept pretty well until I got everyone up at 0100. After breafast we headed up and took it slow all day. The only goal was to get as far as he wanted to go, but he just kept plugging away. You need to keep the younger ones eating and drinking - I think that's key. We summitted safely, got back to Outpost and broke camp. Missed the burger by just a couple minutes.
He is on the day hike team this year and is a maybe for a double Sierra crossing. If I bring him along we will go from Kings Canyon to Onion Valley and back vice OV-KC-OV. That will make it a little easier.
Get the kids away from the video games/TV and on the trail. Keep them fed, hydrated and let them set the pace. Study up on the area you'll be hiking because they will have plenty of questions.
After a couple seasons of tagging along on my training hikes, my boy thinks it's no big deal to grab his boots and go hike 15+ miles on no notice...........................DUG