I get it not wanting to plan out the logistics of transportation and lodging and where to eat. The tour relieves you of those responsibilities. And planning for 7 folks is more than planning for one or two. Consider giving the RS tour office a call and sharing your concerns. Your kids don't seem that young to me, and there are enough of them to hang out together if they want to escape adults - and any seniors like me. I have been on 10 tours, teenagers were on maybe half of them. What do your kids think? How do they want to spend time?
BTW, there is an oldie but maybe goodie video in the RS archives of him travelling with his teens and how they and the adults split their time so as to give each other space.
As to itinerary - well, read closely. There is quite a bit of free time. In addition, if you don't like a certain planned activity, or even dinner, tell the guide you are taking time out on your own. The real obligations are to be on the bus and not hold others up when moving from town to town. Always make sure you tell the guide if you are not participating in something. It's easy.
Another Italy tour to consider is the Venice, Florence, Rome tour in 10 days. You trade off a bit of countryside for three nights in each location, which gives a certain kind of leisure/freedom. And, you have two bus rides vs three - less bus time, more you time.
I like to minimize the stress of travel - each trip is different. If I have been working extra hard, maybe I don't have the energy to plan too much. Sometimes I add time before or after a tour on my own, but it is often when I get on the bus or meet the group, that the vacation starts.
Whatever you decide, I hope you enjoy yourselves.