Welcome from me too!
I'll echo Christine about the need to be IN Rome the night before your flight home if it's from Fiumicino, and it being a bit frustrating getting around the region. Your other challenge is that hotels in Sorrento book up months before high season so you'd want to book a hotel NOW. You do have the advantage of not trying to do MORE of the Amalfi coast! Some options?
Day 1: I'm guessing your tour is the RS "Best of Venice, Florence & Rome in 10 Days" tour? If so, it ends in Rome after breakfast - which you could skip, if desired - so you could head to Sorrento early. Yes, it is possible to visit Pompeii en-route; you change from your "fast" train from Rome at Napoli Centrale to the Circumvesuviana commuter train/Garibaldi Station (attached to the Centrale station) and there's luggage storage at the train station in front of the main entrance and at the scavi itself. We can provide more details later if you decide to go this route.
The train between Naples and Sorrento is a battered unlovely commuter without any creature comforts, may be standing room only for at least part of the journey, and you can't buy tickets in advance but it's cheap and gets the job done. Just keep a tight rein on your valuables but you should be doing that in Venice, Florence and Rome anyway. Some visitors with more generous budgets prefer to book a driver from Naples to Sorrento or reverse. There is also an Express train that some folks have used, its issue being that it only makes 4 runs a day so can be difficult to work schedules around.
https://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule
https://www.sorrentoinsider.com/en/campania-express-train-schedule
https://www.trenitalia.com/en.html
Then retrieve your bags and continue on to Sorrento by same Circumvesuviana train, check in (most hotels will hold your bags if you arrive before check-in time) and spend the rest of the day enjoying Sorrento. Sleep Sorrento.
Day 2: Capri. Set aside the entire day for this, and you'll. be taking a ferry from Sorrento. You do not need a tour (we've spent 2 nights on the island) nor any advance tickets. If you'd prefer a tour, people who've done them have spoken highly of the RS Mondo shared tours. Take a look at the "Capri in Private Boat" tour"? Sleep Sorrento
https://www.sharedtours.com
Current ferry schedules if not using a tour:
https://www.capritourism.com/en/t/sorrento/capri
https://www.capritourism.com/en/t/capri/sor
Day 3: Have an easy 1/2 day in Sorrento, head back to Rome in the afternoon and spend the night prior to your flight. You could also trade out doing Pompeii on Day 1 and do it on your way back to Rome. Either way if you are keen to use a tour for the scavi, Mondo offers one of those too; see the link I provided for the Capri tour. It's a 2-hour tour and the scavi is HUGE so you might want to plan additional exploration time after it's over. Spend some time with the Pompeii website, extensive online guide and maps in advance.
https://pompeiisites.org/en/
https://pompeiisites.org/en/visiting-info/map-and-guide-to-the-excavations/
The other thing you could do on your way back to Rome is visit the National Archeological Museum in Naples where many of the treasures from Pompeii, Herculaneum and other excavation sites are displayed. Closed Tuesdays; they provide luggage storage.
https://mann-napoli.it/en/home-english/
One other option, if not going to Pompeii en route to Sorrento/Rome is the Italo train+bus combo that changes from rail to coach bus at Napoli Afragola station, skipping the commuter train, To view this option, enter "Roma Termini" in the "from" box and "Sorrento" in the "to" box and choose a date and # of passengers. It also operates in reverse (Sorrento to Roma Termini).
https://www.italotreno.com/en
Just a start?