If you're going directly from Rome to Florence (no overnight stays anywhere else) the fast trains are SO speedy, easy and comfortable. After taking an express train of bus into Rome, you'd get on a direct train and be dumped out 90 minutes later right in the middle of Florence: no ZTLs to dodge, no speed cameras to worry about, and no parking costs or availability issues. All 4 of you would get to sit back and enjoy the view out the window instead of eyes on the road. IMHO, it would be a no-brainer for me.
If the timing works, there are a couple of trains which go directly from Fiumicino airport to Firenze S.M. Novella; no need to go into central Rome to catch another train. Those are at 11:08 and 15:08, and take 2 hours, 14 minutes.
With just 2 nights in Florence, you're only going to have 1 full day there so I'd stay in the middle of the city and forego any other trips.