Family of 13 wanting to travel from Rome to Pompeii

Are you talking about day trip/s from Rome to those places? Or are you talking about going from Rome to the Naples/Sorrento area for a period of time and seeing them from there? If you're talking about day trips then, for that large of a group, I would suggest trying to find a tour operator with a large van and driver - may be easier than trying to herd that many people on the train, and you'd have to have a few cars or a very large van or small bus.

By train is faster, but check with a tour operator if they can take your group there for less on a couple of vans.

If you were just going to Pompeii, I could see the argument for taking the train -- though I still think hiring a van or small bus would make the trip more enjoyable, not least because you have to change in Naples. However, since you say "Rome to Pompeii and Amalfi coast," that adds a whole new dimension to the plans, because the Amalfi coast is spread out and not easily accessible by train at all. The nearest train station is Vietri sul Mare, just east of Salerno. Sorrento is generally considered the main transport hub for the Amalfi coast, and it is not on the rail line (it's served by buses and the Circumvesuviana narrow-gauge commuter line).

See https://www.tripsavvy.com/rome-to-the-amalfi-coast-and-sorrento-1547913

Sorrento is generally considered the main transport hub for the Amalfi
coast, and it is not on the rail line (it's served by buses).

While it isn't served by Trenitalia or Italo trains, Sorrento and Pompeii scavi are on the local Circumvesuviana train line. They're also served by Campania Express train during the warmer months, although runs are infrequent. Both of these options do involve a transfer in Naples from Trenitalia or Italo 'fast' trains to the Circ./Express. From Sorrento - which is close to but not ON the Amalfi Coast - you get around by SITA bus or ferries, if using public transport. Both will be very, very busy in June.

The problem with this plan by road is the time it takes to get there and the horrendous summer traffic along the coast. Organized bus tours, say, take much longer to get to Pompeii than can be accomplished by train, and those which include the Amalfi coast are VERY long days for just a couple of hours at the scavi + one A.C. town (usually Positano). You spend far more time on the bus than sightseeing. Maybe private driver(s) could cover ground more quickly but... Maybe drivers from Naples could cut some of the transport time?

Personally, I think the Pompeii is the furthest I'd venture on a day trip from Rome. To do the A.C. any justice at all really requires a couple of days.

I'd agree that it would make a big difference if the OP trying to do this, with 13 people, as a day trip or for a longer stay. It would also be helpful to know the makeup of this group. Young children? Seniors? Mobility issues? Budget might also be helpful. Lastly, it's going to be hot at the scavi in late June!

Kathy, thanks for pointing out the existence of the Circumvesuviana. I've edited my comment to include that.

I also would not consider The Amalfi Coast as a day trip from Rome , especially with this large a group . Even Pompeii would be a stretch , and I would consider Ostia Antica as a more reasonable alternative .