Surely any excursion requires planning; you don't just pick up and go with children in your charge.  How about, as part of the plan, the group leader makes appropriate inquiries of the intended border crossing or US Embassy and gets a pre-clearance?  Everyone needs to show ID at the border so it would be no different to supply ID to US Immigration, get the group cleared, and move on.  If the application is rejected, well, that's the way it crumbles.  Still, there's no need to say who or why the application was rejected, just that it was.