None of those Florence trips are easier by car. Far from it. For the most part you'll find the train faster and less likely IMHO to bore the kids. The kids trapped in the car watching the train wizz by them won't go over too well. Or dealing with getting from a distant parking lot to the city centre.

I'd consider guided tours for those day trips.

They can hit two or more places so you don't have to backtrack to Florence to take a different train or bus. For instance, if you took a train or bus to Pisa, there may not be a direct train or bus to Siena from there.

But a tour bus or a car can go directly from Pisa to Siena. Plus probably easier to get from Pisa to Lucca in a car or tour bus, don't have to find a local bus.

Please listen to prior comments about your decision to stay in Mestre instead of Venice! Don’t stay in Mestre! You have traveled far to visit Venice so stay IN Venice not out in Mestre! Venice is magical all hours of the day and you would miss much of it.

I like Mestre (well the old bits and the parks) but I love Venice proper

Traveling from Malpensa to Lake Maggiore is not a long drive, quite near. . We stayed on south- east coast in Ranco, wonderful.