Hello Wandering216, and welcome to the forum!
It looks like you're flying from the east coast but you still might consider spending the night in Rome the day you land. Sorrento is 4 hours away (best case) and 2 transfers away from Rome at the best of times and that includes the large and busy Naples train station at the end when you're probably going to be most tired. I think planning on staying one night is a really reasonable thing to do. This will also allow to pre-book fast train tickets to Naples - because you'll be in control of your schedule - which means booking at a significant discount from day of ticket buying.
You could rearrange Rome at the beginning of your trip and then use Sorrento as an escape from the chaos and traffic of Rome but you will then need to spend that extra night in Rome before you fly out so it really is 50/50 when you spend that Rome night.
In Florence you might look at Relais & Maison Grand Tour. It is a BnB with interesting and larger rooms - including a upstairs suite room that might work for you. It is well located - two blocks from the Accademia and near the Mercato - if not in the middle of town and well situated near a street to catch busses. We stayed there in 2022 and enjoyed it.
https://www.florencegrandtour.com/
Next year is a jubilee year and everyone is expecting Italy - and especially Rome - to be even busier than usual so I would work to lock down your schedule and arrange rooms as early as possible.
Once you get your dates set I'd look into any festivals, markets or other festa - especially in and around Florence - which is busy with music, dance and other festivals and plan accordingly. This may really be of interest to the younger ones in your party.
Check these events and see if the 2025 schedules are being put out yet:
https://www.visitflorence.com/florence-events/july-in-florence.html
https://www.firenzespettacolo.it/concertifirenze-anteprima-eventi-2024-2025-6891
Even large Italian events can be frustratingly bad at advertising and notifying people about what's happening ahead of time so check multiple sources and be open to certain amount of flexibility and reacting once you get there.
Hope that helps, have a great trip!
=Tod