Santorini + Taste of Italy

It would be much better and less expensive to drop Santorini and add those days to Sorrento and Rome. It is a long distance to travel for such a short time to see that view. Save it for time in Greece.
Sorrento is not on the Amalfi Coast but you can take a day trip by bus there. Take a train from Naples to Sorrento. If you really want the Amalfi Coast, then chose a town there.

Affordable hotels in Oia with a view of the caldera: Old Oia Houses, Olympic Villas

Oia has lots of shops, galleries and restaurants. Do some wine tasting at Sigalas Winery in Oia. You can walk down the steps to Amoudi Bay below Oia for a meal on the wharf and swimming at the end of the seawall that begins next to the wharf. It's the best swimming spot on the island. https://tinyurl.com/y9cx96s7

As you seem to have left your days 'unstructured', it looks doable.

Sorrento as a base gives you easy access to the Amalfi Coast and should you choose, Pompeii or Herculaneum. ( for your "Do as you please" activity)

My husband and I went to amalfi coast last summer for 10 days. We are going to santorini as first stop on visit to Greece this year. We aren't planning to spend any more time than you in santorini but we are then taking a two hour ferry to Naxos while you will spend most of a day traveling to sorrento.

I am thinking you are trying to do too much in Italy in too little time.
We flew in and out of Naples.

Sorrento is a pleasant town but it is not the amalfi coast. We used as a base to explore pompay and climb mt Vesuvius. You can take both a train and a ferry to sorrento from Naples. I also had a couple of friends who took a taxi.

Positano is where the amalfi coast starts. We stayed there and in amalfi.

There are buses that we used. We did not rent a car.

I would map out a bit more what you want to do and include transportation time. I am thinking you won't end up with much time with moving so much.

We too had been to Italy before and throughly enjoyed amalfi coast.

Beth

Since you are flying into Naples, you can get the Curreri bus to Sorrento. It stops just outside the terminal, and leaves you off at the train station in Sorrento. The cost was 10 euros/pp when we took it a few years ago.

Its doable however when its all over your husband is going to be "testy" for sure.

We have done something similar but did a week in Italy and a month in Greece. Now thats doable.
Anyway I am not going to try dissuade you but will provide some tips to make the commute easier.

Santorini. Check with your hotel owner. They may pick up at the airport. They certainly will have a taxi driver relative and can arrange a pick up at the airport. Our hotel ordered a taxi to the ferry port which turned out to be a van with a few other passengers. "The price for the 4 of us was 20 euros flat rate.
$200 US is about the cheapest possible price for a caldera view hotel.

Google airlines that fly to Santorini. As i recall there is a direct flight to Naples. Thats going to be much more efficient than a layover in Athens.

No need to drive to Sorrento. There is a bus and the Circumveneuseua train ( I spelled that wrong) commuter train goes from Naples to Sorrento. For you the bus from the airport makes sense but on the return that commuter train goes right to the Naples train station where you will catch the train to Rome.

As mentioned Sorrento is not on the Amalfi coast so your day doing it as you please means you will need to book a tour or take the public bus to Amalfi.

Sorrento http://www.flickr.com/photos/stanbr54/sets/72157634654031558/