Help with Refining Itinerary for July Trip

I think your kids will be bored in Positano for three nights. I would look at cutting a night out there and spending more time hitting Pompeii or possibly staying in Sorrento instead and catching the ferry for a day trip to Positano and another day ferry to Capri. Positano is lovely, but not a lot to do for kids and is very expensive. We found it to be incredibly touristy, and the stone beaches are not what you are thinking. We think of Positano as more for couples. You kids will enjoy Rome and Paris with loads to do there.

To save time skip sleeping in Sorrento and see Pompeii enroute to Naples. This means you’ll need to take a direct bus to Sorrento (1h) where you can hop on the Circumvesuviana commuter train. The problem with this itinerary is that there’s no room for error when transporting luggage.
Commuter trains are popular for thieves. Not only is it crucial that you pack light, you need to make it hard for a pickpocket to grab one of your bags when the train stops and the doors open. Here’s a website that provides tips: https://www.earthtrekkers.com/visit-pompeii-traveling-rome-sorrento/.
Pompeii opens at 9a Tue – Sun (closed Mon) so I would take the first bus from Positano (I see a current schedule departing at 7:10a taking 1h) and hop on the Circumvesuviana which is where the bus drops you off.
The Pompeii Scavi station is the eighth stop and takes 35-minutes according to this schedule: https://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule?route=sorrento_napoli. I feel the earlier you depart in the morning the better your chances of attracting unwanted attention. When you arrive at the Scavi station you can store your bags. The Circumvesuviana from Pompeii to Naples Girabaldi (downstairs in Naples Centrale station) is the fourth stop. Just be vigilant no matter what time of day you’re on it.

If your budget allows you can hire a driver to take you from Positano to Naples with a stop in Pompeii
Definitely go early, it will be brutally hot in July and there is no shade there

I agree with above. I think kids will be bored in Positano, we were bored after just a few hours
You might consider Salerno or Amalfi or Sorrento instead

I’ll agree that Positano is not exactly kid friendly.
Though it has beautiful views and some worthwhile restaurants, I think the two children would be totally bored with it. The beaches are are nothing but pebbles and everything you may want to see & do requires a series of stairs, not to mention high priced designer fashions. If you want something kid friendly, with beautiful beaches and fantastic spas and plenty of things to do for the entire family, look at Ischia. The ferry ride from Molo Beverello to Ischia is around 1 hour.

https://www.ischiareview.com/things-to-see-in-ischia.html

If you decide on this, I’d head there after Rome, keeping your Naples nights and Pompeii at the end.
To reach the port from Napoli Central and with 4 of you, a fixed rate taxi will be about the same price as the Alibus.

https://www.napoliunplugged.com/wp-content/uploads/2018/03/Tariffe_taxi_2017.pdf

Edit: https://www.napoliunplugged.com/naples-alibus-airport-shuttle

I’ve spent a considerable amount of time in this area since my daughters family lived there for 15 years.

If you do decide on the Amalfi area, do Positano as a day trip. Capri is a 30 minute ferry ride from Sorrento

You may wish to stay only 2 nights in Positano. On your full day there take the ferry to Amalfi and then the City sighting bus from Amalfi to Ravello. Then the boat back from Amalfi to Positano. The views from the boat are spectacular. We enjoyed Hotel Eden Roc in Positano which had awesome views. Then you could hire a driver to take you from Positano to Sorrento and stay in Sorrento for 3 nights. Sorrento is a great base. You can take the ferry to Capri for a day, and also take the train to Pompeii for a day without your luggage along. In Sorrento stay in a hotel with a view of the Bay of Naples. The sunsets are gorgeous. Sorrento also has a lovely Centro Storico area. It may be nice to take the boat from Sorrento to Naples. (The traffic on the drive from Sorrento to Naples was horrendous when went.) Take a taxi to the Archaelogical Museum in Naples and fly to Paris.

Thank you everyone for your wonderful recommendations and helpful advice and links. Good to know that most of you didn't find much to do in Positano so perhaps I will scale my stay there to two nights and spend three in Sorrento instead. I do like the idea of using one day for Capri and another for Pompeii without having to bring our luggage along. The idea of a personal driver is also an excellent idea. I saw another thread where someone recommended a local tour guide to Pompeii so that could be a good option. I will still plan to spend a night in Naples so we can visit the museum and fly out to Paris without worrying about traffic. Thank you again for your expertise!! Just hoping the COVID situation will improve by this summer. The good thing is that our entire family is vaccinated (including my currently 10 year old) and both my husband and I got our booster shots in November. We'll continue to watch the guidance regarding testing and travel restrictions.

Keep on top of Italy's vaccinatqion/booster requirements as they may change.

"The Circumvesuviana from Pompeii to Naples is another four or five stops away."

The station is Garibaldi, downstairs at Napoli Centrale.

The station is Garibaldi, downstairs at Napoli Centrale.

Thank you, I couldn't remember the name and I just edited my post.

Sorrento is a more convenient and what I liked about it was the evening passeggiata (stroll) between 5p to 8p. This is where Sorrento’s families and tourists join in and walk along the main street eating ice cream cones and browse inside the shops. Since you’re traveling with your family, you’ll fit right in.

Thank you for the additional information everyone!! You were very helpful in helping me prioritize the sights we want to see. We are so very excited and hope that things will be ok with the pandemic this summer. Safe travels for those of you who have plans this year! I miss international travel so much, especially Italy!