The Quiet Zone on our trains says specifically "for those who want peace & quiet", then gives the examples of mobiles, loud conversation and 'headphones on silent'. (BTW, no 1st class on these trains, and QZ is only 1-in-4 carriages).
I believe the defining feature to a QZ should be: 'can somebody sleep through this?'. If you have any doubt at all, Don't Do It (or allow etc).
To my mind, children cannot be trusted to be quiet enough for these standards. They might, but you just can't be sure enough. And, yes, I have a DC (3yo), one of the best-behaved kids on the planet out in public. And I still don't bring him into the Quiet Zone.
It'd be doing him a disservice as well. He loves asking about things, spotting the Gherkin, etc, and just wouldn't dig having to keep schtum. In the exceptionally unlikely event we couldn't get a seat in a non-Quiet Zone, we'd stand/ sit on the floor/ whateva.
I commute on a train with a QZ all the time, but the main time I remember was a noisy family in the QZ when I'd just come back from an holiday, during which I'd had a miscarriage. The loudly voiced 'Mummy, why is that lady crying?' still fucking haunts me.
OP, unless you have any reason to think this family had no choice but to be there, YANBU. And if reserved seats ishoo is to blame, scream at the train company.