First, it is a lovely time of year in Italy so enjoy! Assume you are flying in-and-out of Florence?
If you don’t want to rush around and enjoy slower travel, then a one night stay in the Cinque Terre is insufficient, especially since you are hikers and nature lovers. It is lovely there in the villages at night and you can find trails all over that are not too crowded. Just stay away for the sentiero azzurro. That is the one everyone knows about and sections of which are frequently closed.
Consider this so you can balance when you need a car and when you do not.
Arrive in Florence and stay there, making it your base for 4 or 5 nights. Take a day trip to Siena or perhaps to Lucca as well.
Then take the train to a town in the Cinque Terre for 3 or 4 nights. Consider taking the ferry to PortoVenere as well if you stay 4 nights.
After the CT, rent a car in La Spezia and make your way to Montalcino. Base there for 4 nights. Drive to Pienza and Montepulciano, see the ancient abbeys, perhaps hike in the countryside. Parking in Montalcino is easy, just outside the walls.
You will have to spend your last night in the city you are flying out of. If that is Florence, return the car without driving into town, perhaps at Chiusi.
Notice this is 3 places in your two weeks with some time for day tripping, plus a final night somewhere before you fly out. It eliminates any need to try and drive in Florence, which is inadvisable. It is a nice pace. Save Rome for another trip. You don’t have time to do it justice if you want to see Tuscany and the Cinque Terre as well.
If you do not have it already, a Rick Steves guide will come in handy for determining exactly how you want to spend your time, what is open and when, how to get around, where a car makes sense, etc.