I adore Ken, but that itinerary has too many 2 night stays and too much moving about. If you are only going to Lucca to see Pisa, my thought is that you are devoting a large chunk of time and money to see one sight in one town in a country full of vastly more interesting options.
Your kids can go up the Campanile in Venice and/or one of the aforementioned towers in Lucca if you stay there. Have them climb the tower in Firenze. It's a knee killer although only one night in Firenze will leave you frustrated.
Venice - 3 nights/2 full days so you don't have to rush too much. If you get a good sunny day, take the vaporetto to the islands.
Siena - 4 nights/3 full days as a base to see northern Tuscany -- San Gimignano, Volterra, Monteriggioni (great idea Zoe!), and of course Siena itself and a day in Firenze if you like. Stay in an agristurismo outside of Siena so you have easy parking and get a car for when needed (except go to Firenze in a bus). Go to Pisa if you must from here. Alternately, stay in Firenze and take your daytrips...but a car is harder there.
Montalcino or Montelpulciano - 3 nights/2 full days. Drive between the two towns and stop in Pienza for lunch. Fabulous drive, great wine in these two towns.
Rome - 4 nights/3 full days. Drive to Orvieto on your way, drop the car, spend a couple of hours in Orvieto and then take th train to Rome. This gives you 3 days on the ground in Rome, enough to scratch the surface.
I know it is compelling to try to stop everywhere and "get a taste" of everything, but at the end of the trip, you will have changed locations so many times you will lose yourself in checking in and out, packing and unpacking, orienting and re-orienting yourselves. Each time you change location there is a huge loss in time as you try to figure out where you are going and actually go there. How easy are your kids to get out of bed in the mornings and get them moving? If they like to sleep until 10:00, then you relocate, you will lose more than half a day in each transition. Our kids were horrible to blast out of bed even on exciting vacations. If you get a late start, arriving at 4:00pm or 5:00pm in your new locations you won't get any touring done on a travel day, either.