Tuscany with kids - ages 10 and 5

Spend one night in Lucca where you can circle the city wall by bike. The old town is not too big but very lively and there are lots of churches (they do not call it the Little Vatican for nothing) and other sights.

You can visit Pisa on the way to Lucca. With a 2-hour stop you should be able to see its highlights, i.e. the leaning tower, duomo and the surrounding area.

While in Reggello, You are near Vallombrosa and Secchieta. A national forest is there so it's good for hiking. I wouldn't spend a night in Lucca. You already have a full schedule. From Reggello you can go to Pisa and Lucca on a day trip. You can bike in Lucca on that day if you want. Pisa, which is near Lucca, can be visited in an hour. Budget on almost 2 hours each way from Reggello to Lucca/Pisa, once all is said and done (drive, find parking outside the city wall, find your way around).
Near Reggello you can visit Arezzo and possibly Cortona. The Chianti hills are also near.

5 of your 11 days are spent traveling, which, with younger kids, is an all day affair - been there done that. Unless you really like moving around, I would not consider these days as memorable in any way. In other words, you will only have 6 full days to explore. I'd stick to Rome and Tuscany for this trip, or Rome and Umbria (even better as closer to Rome).

Take it from me, your kids will be bored at the Vatican, take them to the catacombs instead.

Skip Venice, you're traveling far too much and with young children it will be a nightmare.

For a stop between Rome and
Reggello, look at Castiglione
del Largo. Cute little beach town with a Castel, stop for a swim and lunch.

On the way to Venice, try Bologna.

Both of these are about half way to your destinations.

Boy, if you can fly out of Venice to home, that would save you a day or two.

A very long day would be Reggello, San Gimignano, Volterra, Pisa, Luca, and back. that is at least 5 hours of driving. I think Pisa is out, although, you could book it for Pisa, then go to Viareggio and hit the beaches, then drive back after dinner.

Here is a suggestion for the trip from Rome to Reggello. Google this archeological site, Carsulae. Here is one website: http://www.bellaumbria.net/en/history-and-archeology/carsulae/

Carsulae is a very low visited Roman ruin. You will basically have your own ruins to play in, on, and around if you stop there. Our family of 12 with three 8 year olds and one 6 year old. They loved it. The kids had a ball playing on the ruins.

If you can you might want to stay in Venice itself. The Lido is a ways out there and you have kind of remoted yourselves. I understand you swim but it is a ways from town.