Driving Rome to Pompeii then to Sorrento

You do not say what month--you may want to avoid traffic. I would not do it because it is just so unnecessary, but if you have your IDP. know the rules like ztls, have parking sorted, and plan on avoiding Naples and the Amalfi Coast, then it is not a big deal to do it.
I would not leave my stuff in a car in Pompeii however. Check bag storage options.

August...so will be busy.
Have IDP so good there...
Will never leave anything in car. And have spots provided by air bnb so won't park anywhere else other than their spot.

Have read a bit about the zones and fines...does google maps avoid these?

Thanks

No, Google maps will not help you avoid ztl. They are signposted though.
In March I'd consider this, in August I'd rather be on the train than stuck in traffic. But good luck and I will be happy to be proven wrong!

We easily drove from Umbria , north of Rome, to Naples. The autostradas are like interstate highways and this trip was much easier, fewer trucks, than earlier drives from Liguria across to Venice and back to Milan.

Hopefully will go smoothly. Do you know if google maps factors in traffic like here in US? Or perhaps Waze works there?

If I'm reading this correctly, you are arriving FCO then renting a car and continuing on to Pompeii.
Touring Pompeii then on to Sorrento. In my opinion, not the greatest way to start a 2 week vacation with kids.

Do you realize this is the equivalent of driving under the influence?

I realize you think you're saving 4 rail tickets, but by the time you include car rental, (€35 day) tolls & fuel (close to € 60) then parking while in the area, the train tickets will be much less.

Save the car for Tuscany.

For driving directions use

https://www.viamichelin.com

ZTLs are not the only concerns driving in Italy
Read this carefully to avoid tickets in the mail up to a year after you return.

https://www.italybeyondtheobvious.com/wp-content/uploads/2015/12/Driving-in-Italy-v1.pdf

Even with 4 people, trains to Pompeii and Sorrento seem preferable and likely time saving. Just getting out of Rome will be challenging. Get your car later to wander around Tuscany.

Good advice everyone. We actually are staying in Rome 4 days before getting car so will be "sober" by then. Will do a bit more investigating with train prices and times, but seemed a lot easier to put the kids and bags in the car than train from Rome to Naples, another train or taxi to Pompeii, then train to Sorrento, taxi to airbnb just west of positano, then reverse.

It's doable, but sober or not, take the train to Pompeii and on to Sorrento. Your kids will enjoy the trains. You will enjoy the trip. The difference in costs is negligible. The difference in aggravation is substantial.

Then I would take the train from Sorrento back to a small town like Chiusi in Tuscany and rent my car there.

Also, FYI, the signage for the ZTLs was obvious to me and my navigator, but not to WAZE or Gooogle Nav.

Thank you, I appreciate it. Will look at the train schedules now. Definitely want to be as low stress as possible. Assumed car was easy but sounds like more hassle than needed simply as transport form A to B.

Before you purchase tickets, look at this offer from Trenitalia.

https://www.trenitalia.com/en/offers/bimbi_gratis.html

If your kids make the cut for the age limit, it could save $$.

Base fare on the fast trains is €48

Base on the intercity trains is €27. This train takes longer but may be worth the savings.

I think the cheapest option would be a train to Naples and then a private transfer to Positano. Ask for a quote online, there is No need to tip: The agreed price is what you must pay at the driver. It might be cheaper than renting a car you won't use, even if you asked the driver to wait for you at Pompeii entrance for a couple of hours.

Since you are staying 4 days in Rome there is no reason to pay the walk-up Trenitalia BASE fare; you can save a lot buyihng 4 SuperEconomy (no changes, no refunds) tickets.

Do not forget to check prices and schedules of italotreno.it/en between Rome and Naples. Italo runs less trains, but their tickets are often cheaper than trenitalia's.

As a side note, you can't trust google maps for planning extra-urban trips in Europe. Use viamichelin.com to see realistic driving times, gas costs and tolls.

On the other hand, Google's Waze is the only app that tries to warn about ZTL areas. Be careful: If you think you can drive wherever you want and if you do not memorize the ZTL sign... Waze or not you'll be fined. The big problem is that locals living and working inside a ZTL can drive into it. If you miss the warning signs following other cars, in 80 meters you'll stumble upon the camera with 5 meters to make an U turn and a line of local waiting for you to make it. At least none of them will carry a gun, but romans and florentines can be a little... Rough?

I'd look into a private transfer from Rome to your place near Positano for a full day, with the stop in Pompeii (and someone keeping an eye on all your stuff while you tour). For your trip back north, look at either a driver (taxi or private) to Salerno - or to Positano and ferry to Salerno. In Salerno you can get a fast train direct to Florence. It's an easy walk from the ferry to the train station - just a slight uphill incline and maybe 10 minutes on pavements.

You're clearly not open to the idea of something other than your home transportation mode. So read up on ZTL, IDP, collision coverages, unattended gas stations, narrow streets and narrow parking stalls, and have at it. You'd rather look at roadside rest stops and signs about attractions 20 minutes off the road, than to sit back and look out a train window.

Your car is going to be smaller than your Escalade at home, and the luggage will encroach on your family. But you'll be in command of your own steed.

I chose to drive back from Tuscany to FCO for our flight home, but it had no particular virtues. A limited-access highway (with frequent construction areas, with even narrower lanes than the U.S. Transportation Agency permits ... ) is a limited-access highway. They're pretty much the same. Having watched the traffic and jammed junctions from our black-car trip from Sorrento to the Naples rail station, I would never drive in Campania.

I'm really mystified by the advice to drive (or ride in a car service) from Sorrento to Salerno. That is a long, slow trip (well, from April to October, anyway), on which some posters here have reported car sickness. (I didn't have any problem in our eight-hour car service tour of Positano, Amalfi, and Ravello.) That's like saying you should drive out to the north fork of Long Island and take the ferry to New London to get to Boston from New York City. Nobody does that.

Pick up the rental car when you head to Tuscany where rail travel is not as abundant. Driving Rome to Naples to Sorrento is an unwise decision because trains will be faster, cheaper and vastly more enjoyable for that trek.

We took the train from Rome to Naples (FrecchiaRossa) it took about 1+ hours. It was fast and super nice, there is no doubt your kids would like it. We then had a private driver from Naples to Positano. On our way back, the driver picked us up in Positano and we toured Herculean which is near Pompeii (kept our luggage in his car) and drove us to the train back to Rome for our return flight. It didn't make sense for us to use up an entire day in Positano driving back to Pompeii and back to Positano again so we did it on our way out. If you'd like the driver info let me know.

Thank you everyone for the advice, and have successfully arranged trains and transfers. Sounds like this will be much less stressful than the car idea.
Appreciate the guidance!

Also any private driver recommendations appreciated-

Also booking the fast train from Rome to Naples was easy online. Do we just buy the regional/local train tickets to Pompei and then Sorrento at the Naples station? Can you reserve seats ahead on these trains or just have to hope you can get seats together as family?
Thank you-