Just to clarify - for anyone who hasn't read through the entire thread - the OP's new itinerary is:
Venice 3N -> Florence (or Siena) 4N -> Sorrento 4N -> Rome 4N
A big improvement over the first stab: Good job, Mary! To do your desired trips to Pompeii, Amalfi coast and Capri, you need 4 nights and 3 FULL days... which you now have. Pompeii will not take ALL day (Nor will you want it to given summer heat; go first thing in the morning!) so take the rest of that day to kick back, spend some time at the hotel pool (yes, book one with a pool!) and generally catch your breath. They close the main street in Sorrento in the evenings so it's a great time to cruise the shops. Head over to Villa Comunale park at dusk with some gelato and watch the lights twinkle on all around the bay below.
Capri has some nice hikes that your family may enjoy. Yes, it will be hot but that's a nice activity for active teens, and a way to escape the mob in the main parts of Capri and Anacapri towns. Just take your time. No tours needed. Give a shout if wanting some suggestions there?
What I'd skip? Blue Grotto. This is why (browse the reviews): https://www.tripadvisor.com/Attraction_Review-g488299-d195537-Reviews-Blue_Grotto-Anacapri_Island_of_Capri_Province_of_Naples_Campania.html
While not EVERYONE came away wishing they'd skipped it, there were enough red flags to give it a miss without FOMO. I also wouldn't plan on spending much time in Positano, if your AC coast trip includes it, as there's very little to do there, and it is reported to have become an Instagram circus since last we were briefly there.
Whether you choose Siena or Florence as your base (I'm an art geek so Florence was heaven for me; for your family, maybe not) you can also take another day trip if one day in each - and you DO need a full day for each) will do ya. Skip the car: you don't need it and don't have a lot of time to go rambling about anyway. Your last day might also be the one for tackling the laundry before heading off Sorrento and Rome. :O)
With all there is to see in Rome, plus the heat and crowds, you'll be glad you tacked on another day! Think about just doing one of the most-visited attractions per day? For instance, do NOT try to do the Colosseum/Forum/Palatine and Vatican museums on the same day. In fact, if your teens find art museums a giant yawn, there's no shame in skipping the overrun Vatican Museums. You could also see if it offers special weekend late hours this season to try and take it on with maybe fewer bodies to contend with and quicker trot to the Sistine. No news on those hours yet but keep an eye on the Vatican's website. Anyway, limiting time spent in the middle of the densest mobs will help manage sightseeing fatigue.