Gosh - but the OP has generated an awful lot of verbiage and a wide measure of opinions, some dramatic, others whacky but most sensible. I guess that's what FT's about, so no surprise there.

But most responses seem to miss the simplicity and generosity of the OP's position.
He doesn't want avios or cash.
He wants BA to say something on the lines of Sorry, we screwed up and we apologise fo making such a mess of your family trip: please pass on our apologies to your son.
He didn't want the classic I'm sure this was unpleasant... etc etc, the unmistakable introduction to the standard BA boilerplate response.

In short, he wants an apology: one that's personal, targeted, specific. It's going to be hard to get that from a monolith like BA without some external intervention.