Wait... hahaha, now I am really confused... But agree with others, stick with 2 destinations on this short of a trip, ok, add Radda to Florence leg , that's 3. More than enough! Hmmm did you cut back on Rome??
Just checking, you had planned to go to Florence directly from the airport, which is doable, BUT stay in Florence 3 nights before Radda? (As stated above, hope you're not considering flying across the pond, train to Roma termini, train to Florence, AND getting into a rental car to drive another hour.)
Based upon your info, you have 8 days on the ground, excluding arrival day (shot by jet lag and getting to Florence), if you spend one night in Florence, 3 in Radda, (which is gorgeous BTW) 3 nights in Rome that's 7 nights and you only have 9 nights, 8 days in Italy, so only 2 days to play with beyond what you've planned.
When are you going, sorry if I missed that nugget. And since we know nothing about your interests, are you keen on museums / foodies / crumbling ruins or perhaps more the 'resort vibe'?
Naples & Capri are another 1/2 day each way from Rome, where you need to be the night before departure to play it safe. Personally, I love Naples & have been to Capri numerous times, but I'm not doing it on this sort of itinerary. You're already in Florence, why not stay in Tuscany another day & add a day in Rome? Seriously there's a LOT to do just in these 2 cities! Really. A lot.