We will depart Sicily this December with the ultimate goal of Rome. Hotels are set for Rome. But would it work to fly from Catania to Naples and do a Pompeii tour and then train to Rome? I just don’t know how to accomplish this. I could stay in Naples one night if required. I have always wanted to see Pompeii. Thoughts?
One possibility. Fly to Naples in the early morning and drop your luggage at the hotel -- assuming they will let you store it. See a bit of the town and stay overnight. Stow the luggage at the train stations the next morning and go to Pompeii. A google search should provide you with a number of tours from which you can choose. Return to train station later in the day for your luggage and then head to Rome.
you could do this without spending the night, but it would make it rushed. The reason for the rush is that the fastest trains from Naples to Rome are cheap only when you have a non-changeable noncancelable ticket for a specific departure.
Between famous pizza and irreplaceable art history there's plenty of other things to see in Naples to make a day out of it if you're not reluctant to spend one night there.
The speedy, cheap commuter railroad from Naples downtown to Pompeii is hot and gritty so you don't want to have your luggage with you but it's a perfectly serviceable, easy way to get to the main entrance (the Porta marina entrance) of Pompeii Scavi, the ancient site.
Oh, just had a thought. If you do spend a day in Naples, you might want to go to Herculaneum too, as it was also destroyed by the eruption.