It sounds to me like they are visiting Florence for the day, driving up from their agriturismo and then returning there at the end of the day. No Florence hotel to help them with the parking.
Hopefully someone can suggest something suitable, and outside the ZTL.
We found parking coming into Siena by just entering "parking" in the Blackberry; between tht and the P signs we found th efree lot. But it's better to have some idea where you are going in advance, especially since you want to be strategically located for your museum visits.
Do you have reservations for the Accademia and Uffizi yet, and if so, what time? That would help people assist you in planning your day.
Also, with kids, you'll need to build in a stop for lunch, even if just picking up foccacia or piadini on the run.