No ... it's not off topic Still ... it brought up thoughts of your own children, and vacations.
So let me clear up a few things.

This was rarely a vacation for them. Sometimes it was fun for them... often it was not.
Being shuttled back and forth between bitterly divorced parents was not a vacation.
I remember walking a little girl to the gate to take her flight and chatting about where she was going and why ... and she responded ...
"I'm going to live with my grandma ... my daddy is in jail and my mom doesn't want me anymore."
Just try keeping tears from your eyes when an 8 year old suddenly confronts you with that.

Those boys, like all UMs, were ALONE, and were placed in our OFFICE where the wall was solid window ... for their safe keeping.
Agents came and went constantly to do paperwork, sit and have a coffee or eat on their breaks ... the children were rarely alone for more than a minute or two, and there were toys and books and a tv, and 2 small couches if they wanted to have a nap.
There was no bathroom facility nearby. They were told to tell one of us if they needed to go and one of us would take them to the public washrooms ... even if they were already 12, and an agent would stand nearby until they had finished.

I myself was sitting at one end of the counter we used for work while the one boy, having said he was hungry, was eating a hamburger and fries, brought for him from the restaurant, was at the other end. I suddenly heard him push his chair violently away from the counter and vomit all over himself and spill his coke in his lap.

The other boy had sat quietly for God knows how long in a puddle of his own pee until one of us noticed.

I was the only male on duty both times.

And I was lucky ... a few other agents had to deal with much worse than vomit or urine.

The children were always upset ... usually embarrassed ... but often afraid of what the person picking them up would have to say about all the trouble and personal embarrassment to themselves the kid had caused ... my 2 boys certainly were.
And exactly how do you think a blubbering 5 year old is supposed to clean himself up ... including a urine sodden pair of undies.
And ... this was an AIRPORT!!!!
We had work to do. This had to be done as quickly as possible and without further upsetting the child. Older ones were far worse time wise ... it could take them forever to do it themselves ...
and they wanted and deserved privacy at an older age ... so an agent would have to be near them until they were done.

So even an 11 year old who doesn't say something soon enough ... can't just run to a toilet to puke in 30 seconds or less.

Boy ... this has gotten a lot longer than I thought ... lol

My original story is missing what was meant to be the end ...
but I thought about it and decided to leave it unfinished in order to get a few reactions before I finished it.

I will finish it ... if anyone wants to hear why I wrote this all in the first place.
Experience is a brutal teacher.