Transport to Positano - long day

A driver from Rome
to Positano will cost a bit but split between 6 maybe not too bad
Train is easy and driver from Naples to Positano is easy
Not sure why you think that is lots of changes?
It’s a train or taxi from FCO to Termini
Then train to Naples
Then driver to Positano

Anyway- we used this company for transfers in the Amalfi area and were very pleased
I am sure there are many others
https://www.topexcursionsorrento.com/?portal_referer_id=46

The above message is right, by train you'll have to transfer in Rome and in Naples; not exactly an Odyssey, you'll have to walk for no more than 10 minutes in both stations. Ask the driver if he prefers to meet you at Napoli Centrale or at Napoli Afragola Station. The latter is served by less trains, but it's not as crowded as Napoli Centrale.

By car it's 3 h and 30 minutes, plus stops. So, it's 4 hours on a van with six passengers and a driver? After a long flight? I'd rather walk.

If you are arriving after April 1, you could take the direct train from Roma Termini station to Salerno and then the Travelmar ferry to Positano.

I think when the OP talks about a lot of changes they’re including that time between the early arrival and meeting their daughter. Maybe they can clarify what the plan was for that time period. However, since she will not be suffering from jet lag, maybe she can assume the responsibility for getting them to Termini. Once on the train, it should be pretty easy. Remembering the traffic between Rome and points south, I totally feel “ I’d rather walk”.

Are you working from an out of date idea that the Naples station is a scary, provincial relic? It is very new and comfortable, if small compared to Rome Termini. 6 people are too many for the Mercedes sedan that took us (and our luggage ... ) from our Sorrento hotel to the Naples Central station. I don'f find vans to be as comfortable as sedans. Are you counting on using an executive SUV with tinted windows? Good luck. The Frecciarossa trains are much faster than any car. Auto traffic from Naples to Positano is always subject to traffic, especially May-September. Positano is not well-connected to Rome.

Don't forget you can also take the train from Rome to Salerno. It is a nicer drive from Salerno than from Naples. Or you can hop on the ferry a short walk from Salerno station (dependent on time of year).
If I were your daughter, I would tell you to continue on your journey, get settled in Positano, and I'd see you in the evening. It should be a snap for her to get there and only delays your reunion by hours.

Valadelphia gives you the very best solution, provided the time of year is right
Ferries start in April but there is also a bus and option of driver from Salerno

We did this trip during Spring Break of 2018. We landed at FCO, had a private taxi pick us up and took us to Roma Termini Station. From Termini we took a high speed train (Italo) to Napoli Centrale and changed trains to the Circumvesuviana train. Monetti Taxi (info on him can be found in the RS guide book) picked us up from the Sorrento train station and took us on an amazing drive along the Amalfi Coast to Positano. For me the varied experiences are what make the trip more meaningful. Navigating train stations are always fun for me and having a private taxi drive us around was a great experience too. Good luck with whatever you decide.

For a car service from Rome to Positano you are looking at €500-600 for a van for 6 people.
It’s actually the better option in my opinion because train tickets for 6 plus a private car from Naples won’t be much cheaper and you’ll save yourself changes in mode of transportation and handling of luggage (on trains you must carry the luggage on board by yourselves).

Another vote for the train to Salerno then the ferry to wherever you are going. Since you didn't mention the time of year you are going, be aware of the times the ferry runs out of Salerno. The ferry is a wonderful trip, and a great way to see most of the Amalfi coast from the sea. Amazing views, and one of our most memorable in our many trips to Italy. Very relaxing. The train station in Salerno is an easy walk with luggage to the ferry dock. Salerno itself is quite lovely as well.

Thank you for all the replies! I laughed at “I’d rather walk than take a car to Positano” - definitely gets the point across. I’m not sure about the Salerno ferry only because I hear if the water is rough, they don’t run it. Something to consider. How does the drive from Naples vs from Salerno compare?

I always add at least 20% to any Google Maps driving estimate. You're traveling in April, so the traffic on the scenic AC road (which is only two lanes, and the busses have to stop and back up to make some of the turns.... get the idea?) may be less than in the highest season. But this area is (pre-Covid) busy all year long.

I was startled to (ICGTFY) have Google Maps offer me a 1 hour 1 min car route INLAND, by way of modern Pompeii - that is, "back to" the route from Naples! When I dragged the route down to the million-dollar view barf-o-ride mountain highway that we all imagine taking from Salerno to Sorrento, it said 2 hrs 2 minutes. Big difference, and that's without any idiots stopping their car in the travel lane to take a picture. You think I'm making this stuff up, but I'm not.

I was startled by the idea for the daughter to travel separately. That is a great idea! Have you asked your hotel for their land-partner, and priced both rides for 6 with luggage? We got to charge our black car trips to our Ambasciatori hotel bill, even the departure drive Ambasciatori to Naples Centrale.

In another thread, I found a post by someone who got carsick Naples-Sorrento, but I personally found it an ordinary highway drive (with only fleeting glimpses of the Gulf in the far distance) on a congested highway. There were some long curves on the approach to Sorrento.