My son and I did Skyline together for the first time on Memorial Day weekend in 2002. He was 12. It took us over 11 hours to hike to the summit and back down to the tram (admittedly, there was a fair amount on basking on top that day). Although we both recall a hot day, Eric still remembers it as a great time and we have done the hike quite a few times since then.
As far as navigation goes, back in 2002 it was still possible to miss the trail on the last, steep scramble up to Long Valley. Today, one would have to be blind to miss it. Or deaf, given the size of the crowds. Navigation is not the problem. At this point, the danger is heat.
So, although I am not the one to be advising against doing this hike with a child (or children), I urge a heavy dose of caution. When Eric did C2C, we had, among many other things, done Iron Mountain a couple of times on rather hot days. In fact, Eric had quite a bit of experience with heat at that point. Otherwise, I would never have considered taking him on Cactus to Clouds.
Maybe these kids are even better prepared. I have no way to judge, since "significant" means different things to different people. However, Whitney (which I gather is on the "done list" from the link in the original message) is a decent start (although not much of a test of hiking in heat).
Back in 2002, we started at 5:25 AM. A much earlier start sounds very sensible. (We voted to be well-rested.

) If the kids are used to early starts (and midnight certainly qualifies), there should be half a dozen relatively cool hours to gain some altitude (although it should still be plenty warm this weekend).
If Kurt Wedberg knows these kids and does not think the plan is nuts, that would carry a lot of weight with me.
Best of luck all the way around on this one.