Agree about potentially flying into Florence as the above poster mentions. Have you already bought your flight?
4.5 effective days to try to see Florence, Tuscany, and Cinque Terre? Wayyyyyyy too much. I would eliminate Cinque Terre from your intinerary and save it for another trip. Florence and the greater Tuscany area has more than enough to keep you occupied for that time period.
You could fly into Florence. Spend all your nights in Florence and then easily take a day trip or two by train to Siena or one of the other Tuscan towns (Luca, Pisa, ect). Florence alone is good for 2-3 days. Then train from Florence to Rome. Spend your three days in Rome before moving onto Sorrento. At the end of the trip, you could fly out of Naples or return to Rome.
If you’re stuck because you’ve already bought flights. I would seriously consider just spending more time in Rome (more than enough there to occupy a week, much less three days) and then spend the rest of your time in the south. Could go to Positano. Could explore Naples. Pompeii/Herculaneum is near there. The Almafi Coast in general. And then still fly out of Rome or Naples.
11 days really isn’t enough time to try for all the places you want. We spent 18 days in Italy last year and only covered Rome, Florence, and Greater Tuscany. And even then, we could have spent a week longer there, had time allowed.
If it were me, I’d be picking north or south of Rome only. (Sounds like South would be your choice if you’re trying to meet up with family.) There is plenty in either region to keep you occupied, so you shouldn’t worry about filling your days.
