Florence to Pompei Scavi via train

I think the only way to do this without exhausting yourselves would be to take the train to Naples, stay overnight and maybe visit the excellent archaeological museum there ... which is where most of the treasures excavated from Pompei are housed. Would be a good preview for the visit to the Scavi the next morning. The Circumvesuviana is the better choice - would drop you right at the entrance to the diggings.
Could then head back to Florence that afternoon.

You are right, the Circumvesuviana is a locally owned company whose schedules are not displayed on trenitalia.com.

In summer, with children, your friends should take the Circumvesuviana tourists' train. It uses the same tracks and stops, but it's air-conditioned. Since it costs more and the departures are less frequent, daily commuters do not use it. Note that the Circumvesuviana calls at Herculaneum before Pompeii.

From Firenze SM Novella to Napoli Centrale they can either travel with Trenitalia or Italotreno.

Taking the train from Florence to Naples and then the Circumvesuviana train is probably the simplest choice.

Here is a site with a schedule for the Circumvesuvana --https://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule --
appears a train leaves Naples about every 25 minutes, for the 40 minute ride.

Anyway, let me know your thoughts

It seems you are not spending any time in Rome otherwise going to Ostia Antica would a much saner way to get your "ancient Roman city ruins" experience.

You may want to look at Ostia Antica as it would save 4-5 hours of train time. Also there is some shade at OA, which in the middle of summer will be welcomed. Pompeii is pretty much a 'shade free' zone

Aaron, I'll agree that the best way is a fast train to Naples, and then the Circumvesuviana to Pompeii Scavi-Villa dei Misteri station, very near the main entrance to the excavation.

That said, and acknowledging that you already know it would be a long day, there's NO way I'd take this on as a day trip from Florence, and especially not with children. It would involve approx. 8 hours RT sitting on transport that could be MUCH better spent sightseeing in Florence...or at least something much closer TO Florence than an attraction that's not even particularly close to Rome.

Summer? The scavi is going to be hot, and there's little shade. Between the heat and many hours spent just sitting, the kids could be miserable, not to mention the grownups. Nope, I don't see taking the trains to be a "refreshing" way to do this from the distance your party is wanting to do it from, and I wouldn't do it by road either as that could take even longer. Save it for a future trip when Pompei and other locations in that region can be given the time and attention they merit. It's just much too far for a day trip to a single attraction.

but some in our party are interested in seeing Pompeii (including kids).

"3 kids ages 1-8" from a previous post; ( so will be 3-11, 4-12? ) when this would happen.?

If I were dared to do it, there would have to be cash prize of at least 6 digits to even think of doing it.

Firenze SM Novella to Napoli Centrale, then downstairs to Napoli Garibaldi for the train to Pompeii Scavi. However this makes no sense—about 7.5 hours on trains.

There are times when you have to tell people that somethings just don't make sense. This would be the time to do a reality check. That's an oppressive amount of time traveling that would better spent in other ways. While someone hard-core and nimble might power through, it would be really hard on the kids. Think of it as one more incentive to make another trip to Italy. This is exactly what we're doing on our next trip.