I also think Pisa might be far for you, but it was to give you an idea... most generally it can be done, but moving around or having a more central base.
8 adults to the 2 kids should work out fine! But still, remain flexible with your plans. I think a mini van or two cars might work best, particularly with 2 car seats. Make sure to request them ahead of time, if you're not flying with them.
Once you're in Cortona, I'd just simply suggest heading to the local tourism office - they have contacts with all the local estates, know which ones might be open and easiest to visit at that time. They will also be able to recommend locally-based tour companies that might offer some interesting itineraries, those can generally be booked a few days ahead of time. So a stop at the tourism office should be among the first things you do once you arrive
I suggest taking it slow and concentrating on the local area, which is quite off-the-beaten-path once you leave Cortona. There are many small hilltop villages in the area, which are charming and offer great traditional dining. Around the holiday season, there are nativity scenes set up in many churches, and small Christmas markets on the weekends. In the area I'd suggest making your way to
Arezzo, Sansepolcro, Anghiari, Castiglione Fiorentino,
Sarteano and
Lucignano... in addition to some shopping at the Val di Chiana outlets (although being around Christmas might be quite packed right before the holiday) and to Montepulciano, Pienza, San Quirico and Montalcino. In essence - I recommend taking more time to wander around the immediate area than to trek across Tuscany to go to Pisa and just see the tower. Although if you do fly in or out of Pisa, it would be a pity to miss it! It is definitely to be seen, at least once in a lifetime ;-).