Our dream vacation

Looks very nice, but Orvieto belongs between Rome and Florence, unless you want the fast train fron Rone to Florence and then backtrack.

We wanted to do Florence right after Rome and we're OK with backtracking to Florence or I think we can fly out of Pisa to Taormina if that's how we decide to get there. It just seems like a very long train ride from Florence to Sicily so I think we will most likely fly. I guess we could head to Rome and fly out of there as there's probably more options from Rome.

Ok, good. We loved Orvieto!

I am afraid I cannot help with your Sicily question as we have not been south of Rome--- and that wasn't until our trip last fall, our 4th to Italy.

You are backtracking back and forth. You should map your destinations on a map and go on a north to south order. In your case you should try to fly to Florence then work your way south (Florence Siena Orvieto Rome Amalfi Coast). Sicily (Taormina) is rather far. The best way to reach it is by air from Naples or Rome. From Salerno it would be an all day (or night) trip via train+ferry (or just Ferry from Salerno to Messina, then train or bus to Taormina).

We don't have a choice but to fly into Rome so we are basically going to start there, go north and then work our way south. We are actually staying in Taormina for 6 nights not 2, as this is going to be our down time and relaxing part of the vacation. I looked back and we are actually in Florence first, then Siena and then Orvieto so I think it might be best to head to Rome and then fly to Taormina from there so that we're not wasting too much time travelling. Thanks for your comments.

There is no airport in Taormina which is indeed very small.
The nearest airport is Catania. I have been there for years in August for my holidays. It is usually very hot and very dry in the summer, often around 38-42 degrees Celsius. I once went in October, wonderful weather but maybe a little too quiet, June or September should be perfect.
You asked what would be the cheapest way to go to Salerno.
You need to check but a cheap nice but however slow way, would be to take the boat from Messina to Naples, you would then have time to enjoy the Mediterranean Sea and enter Naples by the bay. Easy train and bus connections from Naples to Salerno. Another way is to take the train in Taormina Giardini Naxos to Salerno. The train takes you to the Strait of Messina (you take the boat there) which takes you to Reggio di Calabria and from there direct train to Salerno. If you want to check, download Trenit app, you'll see fares, timetable. In the South of Italy, both planes and trains are often late, so take this in mind when designing your timetable.
Your timetable looks really good. Enjoy your vacation.
If you need some further info on accommodation both in Catania and Florence, let me know. The last hotel I was in Taormina was really nice, I have to see at home it's name.
Or then fly from Catania to Naples airport

There are plenty of planes between Rome and Catania, so that's a good option.
I know a good taxi driver who come and take us at Catania airport even at midnight, so if you need let me know.

Rome - 4 nights
Orvieto - 2 nights
Siena - 3 nights (change train from Orvieto at Chiusi)
Florence - 4 nights
fly to Sicily (Vueling has direct flight from Florence to Catania)
Taormina, Sicily - 6 nights
fly to Naples
Salerno - 4 nights

Thanks for the great tips! We have a beautiful Airbnb on the hillside in Taormina with our own private pool so hopefully that will help beat the heat! I was aware that we had to fly into Catania. Unfortunately one the people we are travelling with isn't crazy about the idea of a ferry so we'll have to nix that option. It sounds like the train/ferry/train may be the best choice. We will be spending enough time in Salerno that will allow us to see some of the Amalfi Coast. Thanks again!

I just had another question, most of the group is not crazy about renting cars while in Italy as no one wants to be responsible for driving! I'm wondering how difficult it is to get around Sicily to sightsee if you don't rent a car? Not exactly sure what we want to see yet but it's looking like that will depend on how easy it is to get around.

I often use public transportation to get around Sicilia if I travel solo, with friends we rent a car. Driving in Sicilia is easy (except for parts of Palermo and in some hill towns if you are not used to that). A car will make your time more efficient.

Sounds like a fabulous trip.

Regarding rhe Salerno portion of your question

While based in Salerno we want to see Positano, the Amalfi Coast and Pompeii. Is this too ambitious??

Pompeii is doable if you take the train to the town of Pompei, then grab a bus or taxi to get to Pompeii Scavi, the site of the ruins.

The Amalfi Coast up to Positano is easily done by bus. Don't miss Ravello, high on the hill! Villa Cimbrone is worth a visit.