No qualms about trying to juggle kids and riding the metro in Naples for the first time?
I guess that's a question. I meant "include attractions of interest to kids of unspecified ages, to get them to try an ancient city." But if you mean, "Will my children be abducted on public transit in Europe?", you said that you have plenty of travel experience. No one gets abducted on the New York City subway! Unlike Sorrento, Pompeii Scavi is not the end of the line, so you need to tell them where to get off if they happen to get separated from you. But nothing separated my wife and me on our multiple Circumvesuviana trips. Remember to validate your ticket before boarding.
Do you understand that the Naples Metro and the Circumvesuviana (and, for that matter, Trenitalia) are all different products, probably run by different agencies? We did not use the Naples Metro, because we like walking cities new to us. We walked about 1.5 miles from our hotel to the Naples Central Station, to pick up the Circumvesuviana to Sorrento. (We had left our luggage at the hotel on checkout, and first walked to the Archaeology Museum, before lunch. I will say that the wait for a pizza table [at Gino Sorbillo, in our case] was kind of a festive crowd occasion, although a bit hot in the sun.)
It is hard to overstate how crowded the Circumvesuviana is. In my opinion, the much-ballyhooed "pickpockets" were unable to reach us, because the crowd was completely impassable. The real struggle is to get your luggage (if you are just arriving) close enough to you to keep an eye on it, while not blocking 120 other people from getting in and out of the train on the 12 (made-up number) stops before Sorrento. Well, Pompeii Scavi isn't quite as far from Naples, same line as Sorrento.
I imagine the Circumvesuviana is particularly intimidating for first-time European visitors who have never used public transportation in their home country. But in 23 years living in NYC, I have almost never felt as crowded on the subway as I did on the Circumvesuviana. I do remember when the NYC subway was not air-conditioned, like the Circumvesuviana is, today.