I don't have children (to my knowledge) but I would imagine that such an occurance would indeed cause a degree of trauma in most parents.
Given the extenuating circumstances - where each parent is obliged to use more than one vehicle - then such confusion can easily arise - it doesn't make them anything more than a victim of such circumstances.
Should the CPU people accompanying the 'First Family' have caught this? Well, depending on the brief and the number tasked to accompany the family on what I would have assumed to be a 'low-key' luncheon, they every one, as much as the parents, stood every possibility of falling victim to cross communication and assumption.
Performing duties like this was a pain in the arse - especially where families were involved - as there was only a certain point one could go to when advising of potential security vulnerabilities and accommodating them in terms of manpower, equipment and behaviour; should the brief have indicated a creep beyond which the presence of the security people could possibly have been considered to be intrusive, then this was always the point when things got to be difficult between the protectors and those needing protection. People like to be protected but not inconvenienced.
Insofar as the timing of the revelation is concerned this may well be a pre-emptive announcement as a result of an enquiry to the press office following a third party report to the media about this ‘sordid lapse’ in parenting responsibility.
