We're planning a Florence, Rome, Sorrento trip for May, with the kids. September should be great. I don't think you'd fly into Florence with that itinerary because you don't want to backtrack on your travel and Florence is between Rome and Venice. Last time we went, we flew into Venice and out of Rome, with Tuscany and Capri in between. It takes a while to get to the Venice airport from the tourist areas and it was a brutal place to fly into after being on a plane overnight.
We're hitting this place up for a couple of nights in Rome:
http://www.romecavalieri.com/ , but other than that we're booking airbnb in Florence since we have the kids and a hotel in Sorrento. Planning to visit Tuscany sites from Florence and Capri/Amalfi/Pompeii from Sorrento.