We did something similar, from Syracuse to Sorrento. We chose air...Bus to Catania Airport, Ryanair flight to Naples, Taxi to Naples station, Circumvesuvia to Sorrento. Due to covid requirements, we left plenty of time, but I recall being in Sorrento mid to late afternoon, probably could have done it as follows...Bus to airport 1 hr, check-in/security/wait 2 hours, flight 1 hour, getting to Sorrento 1.5 to 2 hours...so maybe 6 hours. That slog from Naples to Sorrento seems really slow, but you could head to Salerno and head up the Amalfi coast that way, and probably save time, or arrange a driver from the airport.
You could probably do that trip from Taormina in a little over 6 hours by train and taxi, you save by being a bit closer to Messina, plus can reach Amalfi via Salerno rather than going through Naples. Timing may also play an issue, late March is a bit off peak season, so trains and planes may be a bit more infrequent, meaning having to wait at changes.