Transfer from rome to sorrento.

You're right, that would be a lot. Herculaneum is smaller and probably a better bet if you're on a schedule. We were in Sorrento for 2 weeks last year and spent a day in Herculaneum and 12 hours over 2 days in Pompeii. We didn't make it to Vesuvius but from everything I've read the driver can only get you so far and then it's still a half hour hike or so to the top, so mobility challenged people may have a tougher time.

Pompeii is only a 35 minute train ride from Sorrento so it would make sense to do it on another day when you have more time. Keep in mind both Pompeii and Herculaneum have very uneven surfaces and high curbs that could be challenging with mobility issues. We used Mondo Tours for our day in Pompeii. The guide met us there as part of a small group tour that we joined. https://www.sharedtrips.com/shared-city-tours/pompeii

Good advice from Allan, IMHO. Trying to do all 3 sites en route to Sorrento would be much too much, and it promises to be plenty warm in mid-May as well. As he has helpfully pointed out, Herculaneum is more compact than Pompeii (which covers a vast amount of ground) so would be the easier of the two to work into your journey.

Honestly, I'd skip Vesuvius altogether. As he has pointed out, from the drop-off point you'd still have an uphill hike on a loose surface that has been troublesome for some visitors, and you would need advance, timed-entry reservations: you cannot buy tickets at the gate.. Any delay, such as a traffic jam, could jeopardize missing your time slot. You can see what's left of the cone clearly looming over Herculaneum, Pompeii and other locations around the region.

Yes, I'll recommend day-tripping Pompeii from Sorrento too. It is not difficult by (battered, not particularly comfortable but cheap and serviceable) Circumvesuviana commuter train. Then you won't feel you have to rush. If you take the tour he has recommended, you could also stay on for more exploration after it wraps up, if desired.

Worth mention? While there are 4 of you to split the cost, you'll need to factor in the wait time for the driver while you visit Herculaneum. Given the distance from Rome, I wouldn't expect it to be inexpensive but, well, our budgets are all different! :O).

Alternative and less expensive option would be to take fast train from Rome to Naples and have driver pick you up there

I’d also suggest day trip to Pompeii from Sorrrnto-it’s pretty easy and your above travel day is sort of long already

We used this company for driver from Napoli Centrale to our hotel in Sorrento
Cost in 2019 was about 100 euros

www.topexcursionsorrento.com

Also used Mondo Guides for a guided tour of Pompeii and were very pleased
www.sharedtours.com

You have a lot of research to do, but you are an FAQ, so you can use the site's search box, blue area top center. Use keywords like "Sorrento or Amalfi Coast", "Naples to Sorrento", "Naples to Positano", and similar. This area books up at least six months in advance, so do not put things off too long. It is already very crowded by the middle of May. And you need air conditioning by then. BTW, Sorrento is not a "beach" town, but the fancy hotels on the cliff front have elevators to fixed boardwalk swimming platforms in the Gulf of Naples. Of course they have pools too.

Vesuvius is out of the question. Besides, what's important is seeing Vesuvius FROM someplace that it buried! If the mobility issue is the least bit important, you should know there are very long gradual concrete ramps to descend one story to Herculaneum. Herculaneum is not "better" than Pompeii, it's just both smaller and easier walking, although there are Roman era paving stones (at least as bad as cobblestones in modern Europe) at both. There are vast undiscovered parts of both Pompeii and Herculaneum, and since they are under modern cities, they may never see the light of day.

I have often thought that Oplontis would be a good substitute for someone with substantial mobility problems, but it is relatively small (IF VERY LIKE the Getty Villa in California ... but for real.) And no one at a cocktail party asks you if "you went to Oplontis?"

Have you plugged your trip into Google Maps? I can't see any reason for sitting in a car for three hours Rome-Naples when you could take an air-conditioned train for 1:05. And you'd save hundreds of Euros on the charge. Will your luggage fit in a five-seat sedan with all of you?

It is slightly tricky to get to the Sorrento and Amalfi Coast area (don't say "Amalfi", that's the name of a town), but it is much more complex to get to Sicily. That is a project, even from Rome. It's probably harder from Sorrento.

https://community.ricksteves.com/travel-forum/italy/amalfi-coast-for-7-nights-itinerary-help

https://community.ricksteves.com/travel-forum/italy/naples-to-sorrento-train-or-private-driver

https://community.ricksteves.com/travel-forum/italy/herculaneum-and-pompeii-questions

https://community.ricksteves.com/travel-forum/italy/pompeii-and-vesuvius-69e8366c-1e75-4a14-a0bc-0677269492d1

https://community.ricksteves.com/travel-forum/italy/amalfi-coast-for-5-days-where-to-set-base-from

https://community.ricksteves.com/travel-forum/italy/one-week-on-the-amalfi-coast

I have often thought that Oplontis would be a good substitute for
someone with substantial mobility problems, but it is relatively small
(IF VERY LIKE the Getty Villa in California ... but for real.)

Oplontis is outstanding https://pompeiisites.org/en/oplontis/, it might be a great stop on the drive down. We took the Pompeii shuttle bus to it after a few hours at Pompeii, and then the train back to Sorrento. It was a rich guys villa that would have belonged on Lifestyles of the Rich and Famous if there were TV's 2000 years ago.

Just for completeness, Oplontis is easily accessible by (hot, jammed) Circumvesuviana train from Sorrento. It is not as easy to get to from Positano or other places not right on the Bay of Naples. I mention this because stopping at Herculaneum for two hours (?) would add substantial cost to the car and driver project.

I realize why you think of it as "on the way", but we stayed 5 nights in Sorrento specifically because it has such good daytrip connections, unlike many other towns in the area. Of course it would cost a couple of hundred Euros to book a taxi or black car from Sorrento to Herculaneum and back, with a two hour wait, as well.

Thanks much for the comments and suggestions. Will certainly incorporate them into our final itinerary!