My two cents, based on your other thread, is that since you intend to only have two lodging bases, you can do all this by train, or bus if needed. If you have a special thing you want to see one day, there's no reason not to rent a car just for the day to simplify matters (assuming you will bring or rent car seats). Trains are easier for everyone, tired parents and active little boys both.
BTW, the arrival airport will definitely be Malpensa, as Linate is still closed for renovation.
Edit: since most of the train travel will be on regional Trenord trains without advance purchase discounts, you haven't missed much in terms of cost savings opportunities. Trenitalia is easy to use to look up train connections.
However, Pienza doesn't have its own train station - you get off in Chiusi/Chianciano Terme and take a bus connection. That might be an opportunity for a car day if you prefer. The bus won't be hard to find outside the station, but with 2 wriggly kids and luggage, it's an extra step.