Tuscan Driving Itinerary

For pretty scenery, I would drive on SR 222 to Siena (to save a few minutes you can join it from SP3 off the main Florence-Siena dual carraigeway), then take the dual carriageway to Sinalunga for Montepulciano.
Pienza is right next to Montepulciano so it seems easy to visit it right afterwards. However, Montalcino is 5 miles off the main road so it is more time consuming: you could skip it if the day feels long.
Monteriggioni is very tiny and there is an expressway exit right next to it, so you should have time for it at the end.

Your route makes sense, but that's a lot of time in the car and not much time for exploring each stop. That loop will take 6.5+ hours over two days of pure drive time, and risks mutiny from the back seat unless your kids are couch potatoes. You might consider cutting two of your stops on day one to have time to check out the towns you don't cut and Colle di Val d'Elsa itself. You're also going to be driving through Val d'Orcia (very picturesque.)

Montalcino is cool if you've never been, but probably the most crowded of your choices, and there's an overhead getting in/up there. Monetriggioni might be similar. Less is more. And you can always play it by ear based on weather and how everyone is feeling. Good luck!

That Monteriggioni exists is interesting as food for imagining history - that a little set-piece like this was created and how its features were needed for defense and for the needs of its citizens. Beyond that it's just a few shops and a lot of tourists from bus tours.

In my experience, visiting Montepulciano and Pienza in a single sunny day is enough. Start driving on A1 to Valdichiana/Bettolle exit; the day is long enough and you cannot afford a longer and slower itinerary. Visit Montepulciano, maybe lunch there and move to Pienza. Pienza is much smaller than Montepulciano (but IMHO more interesting) so a couple of hours are enough. After that you can back up to A1 and Florence, or if it is early enough you can go back through Siena, maybe having an half an hour stop in Monteriggioni (but this makes the return trip much longer). - Skip Montalcino as there is no way to visit four destinations in a single day, not even if you were transported there on the instant.

I would lose Montalcino, unless you absolutely must buy Brunello wine.

Follow lachera's suggestion.
A1 freeway to VALDICHIANA exit at Bettolle > Montepulciano > Pienza

If you made good time, pass by Monteriggioni on the way back to Florence. Monteriggioni can be visited in one hour, including the time to park and walk inside the wall.

If, at the end of Monteriggioni's visit, you don't have time anymore, just take the freeway back to Florence from Monteriggioni (one hour drive)

if you have more time, you could also drive from Monteriggioni to Castellina in Chianti and take the Chianti Road (SR222) back to Florence from Castellina via Greve in Chianti. It's one extra hour drive compared to the freeway (if you make no stops along the way).

FLORENCE > MONTEPULCIANO > PIENZA > MONTERIGGIONI > CASTELLINA > GREVE > FLORENCE is a 5 hour drive loop (without stopping even for pit stops).

So if you want to visit all of the above, you have very little time to stop at each.