Ok folks, this week I took my 100th flight of the year, so please believe me when I say I think I've seen it all at Security! Let me assure you that I have never seen a child removed to a "private" room or even outside the immediate screening area. Many airports now have the open ended cubicles, but most have the additional screening area right out in the open. I've never seen them take a child so far that you couldn't see them, and I've never seen them deny the parent the right to be within a few feet. I've seen parents ask politely if the screener can wait to re-screen the child until they've gathered their belongings, and I've not yet seen that request denied.
It is true, of course, that there are some hard-case security people, and some airports seem to attract more of them than others (like DIA), but for the most part, they want to be reasonable and they want to get the search over quickly.
NotUrsula has the procedure down pat, and we can learn from her. We must also do our best to make sure our children are prepared and not nervous about flying. IMHO, most of the time when I see a nervous kid, I see a nervous parent, too. Make sure not only to tell your kids that they might get screened, but that you might too, and that if you are, they need to wait where the agent tells them. It will almost assuredly be within sight, and they need to know not to worry.
With respect to why you can't stand close, the other reason is because if you're too close to the machine, you could inadvertantly set it off. It just delays the process.
With respect to shoes, TSA has a new policy on this on their website
www.tsa.gov. Everywhere I've been the last 2 weeks (MCO, PIT, PHL, LGA, BOS, MHT, ROA) they've suggested removing shoes, but have not required it. Since so many shoes, even the cheapest of the cheap Payless deals, have metal in them, take them off the 1st time unless you know for sure. As you come thru Xray, ask the agent if your shoes have metal. They'll be happy to tell you!
Remember, the VAST majority of people pass thru Security without being stopped.