I can't understand why you'd go all the way to Sicily for just a couple of nights - I think you've seriously underestimated the sightseeing there. And take lucapal's advice above - he lives there.
Assuming you've opted for just 2 nights in Florence, consider going by bus to Siena - they run hourly and take 75 minutes -and the following day hire your car for a couple of days drive to Rome's Fiumicino airport. Check the search box at the top of this page for suggested itineraries along the S2, but along or nearby are Pienza, Montepulciano, Bolsena, Viterbo to name just a few places - if you can find a vacancy at this late stage, consider a night or two in an agriturismo (farm stay). Make sure you know where to dropyour car at Fiumicino - most car hire bases are in long stay multistorey car parks B and C. Then fly Fiumicino to Sicily if yoy've decided not to spend time in Rome.