Rome to Tropea to Taormina and back

if you do not split your time in Tropea, you could fly from Catania to Napoli. This eliminates some backtracking, but you would probably need separate car rentals. It's a time-versus-money question.

From Napoli you can go to the Amalfi Coast, which is a shorter trip than from Tropea, and you already will have covered that ground on your way to Tropea.

I am a little confused. Tropea doesn't seem to be a ferry port, nor does Taormina. How are you planning to transit the Straits of Messina? As far as I am able to tell, the Italy/Sicily Bridge is a non starter. This seems hugely ambitious. Similarly, the route from Tropea to Sorrento, for example, is a pretty long jaunt. How many days?

For staying on the AC, Sorrento is a great home base. Pompeii is not a beautiful town. Suggest Sorrento with a train visit to Pompeii.

How much time do you have for this? These are considerable distances.

Car ferry from Villa San Giovanni to Messina Marittima.

ViaMichelin estimates a driving time of 7 hr. 15 min. from Rome to Tropea, and that includes no stops, no getting lost, no looking for parking and no traffic.

As far as I know, cars can be taken on the ferry across the Straits of Messina. But it has been mentioned that car-rental agreements often prohibit taking the vehicle on a ferry, so that's something that you'd need to check out ahead of time. It would be simpler to hop on a train, though it would take longer. I took the overnight train to Catania (a miserable experience; avoid that night train) a couple of years ago, and it ran hours late because of construction work around the port. I have no idea whether that is still going on, or whether cars and ferries might also be affected.

I love Sicily, but my comment to you is the same as my comment to anyone planning to go there for a very brief visit: Please do not do it. It is a fascinating island with wonderful sights all over. To go just to see Taormina and a winery...why? To me, that is like going to Italy just to spend one day in Rome.

Thanks for all the comments and advice. We have 2 wks. We are spending 3 nights in Rome (3.5 days) then have a time share in Tropea for week. We can just do some day trips from there but thought it would be fun to ferry to Messina and have a quick visit to Sicily. Our friends have asked to go to the Gambino Winery but this all just may not be doable. Driving to Tropea is less time, money and offers much more flexibility than the train from Rome. We may just do some daytrips out of Tropea instead of trying to get to Sicily. I have toured Taormina and Mt. Etna but none of the others have. After the week in Tropea we will drive back up the coast and stop somewhere in the Amalfi/Positano/Sorrento area for two nights and then drive to Pompeii (the only place we all have as definite on our list) for a day visit before returning to Rome to fly home the next morning. Does any of this make sense? I am confused about how we are backtracking if we go south from Rome to Tropea, continue south to Sicily and back north to Tropea, Amalfi Coast, Pompeii to Rome.

Just wanted to add that a 7 to 8 hour drive is something we do on a regular basis from our home in Atlanta to visit relatives and friends. Long drives are a normal thing in the States. This entire trip is planned around our apartment in Tropea having been to Rome and points north on another trip.

Makes sense to me. Just check the ferry info (and car rental info) as suggested.
I would not want to drive on the Amalfi Coast in May (though certainly not as bad as summer would be). You could stay at the Salerno end so as to avoid getting stuck in that traffic. There are several cute and low-key towns, and it's easy to get to Pompeii from there as well if you want to use the train.
Be sure you have your international drivers permit from AAA, know about ZTLs, etc.

What is the name of your timeshare in Tropea? We stayed a week in one (I can't remember the name right now but it's up on a hill above the town) and there was a bus tour to Taormina that our friends took from the resort They really enjoyed the day. We didn't go with them because we already had 10 days booked there after our stay in Tropea. We did take the train from Lamezia Terme to Villa san Giovanni and the train transferred on to the ferry and then on to Catania where we were met by our AirBnB host. It was a very slow travel day. We hope to go back to Sicily again as we enjoyed it so much and didn't see all we wanted to see. If we go back we will definitely fly one of the budget airlines within Europe to and from Sicily. Feel free to PM me about your resort.