For your Rome visit, I would generally plan on one day for the Vatican Museums and St. Peter's, and one day for "ancient Rome." And if you have time/energy/interest after that, then you can fit in other things.

I consider Galleria Borghese to be a must-see for me and my family, but that's because I really love it, and we all really like art. It is smaller than, for example, the Uffizi or the Vatican Museums, so two hours is a doable timeframe. But this is one of the few places that you need to book in advance, so do you really want to commit that time to it? And it is out of the way of most other things in Rome. When we took our DD to Italy, I waited on this, as Rome was at the end of our trip, and I wasn't sure how many museums she'd want to visit. So midway through our trip, I just went online (we were travelling in October)and booked the tickets then. You could do a similar plan.

In terms of what to see near "ancient Rome," I would definitely include San Clemente, because it's so fun. After the Forum and the Colosseum, your group may be out of steam for more ancient times. And I very much agree that Rome: Past and Present is an EXCELLENT book to get; otherwise, it's very easy to look at the Forum area as a bunch of stones.

And the cat sanctuary is not too far from there, either.

In terms of visiting some place like the Pitti Palace or Palazzo Vecchio (which, to be honest, I didn't even know it was possible to visit), I don't know that it's worth your time if you want the kids to experience a palace. BUT, the Doge's palace in Venice, which I believe you're planning to see, will be a good example of that type of thing. And if turns out they like visiting palaces, then you could visit more later on in your trip.

You do have a lot on your list for Rome, but I think your approach is good. Plan one big thing, then do or visit other things as you have time and energy. We always stay near Piazza Navona, so are closer to the activities near there. But every evening, we spend time in Piazza Navona and/or the Piazza where the Pantheon is, and also usually go to either the Trevi Fountain or Campo de' Fiori. We stop at a cafe at one of those places. That kind of experience doesn't take long to enjoy (though of course you could spend hours sitting at cafes), and you can add and subtract from the list as time and interest allows. I would suggest visiting those places near the end of your day (but early enough to make a quick stop INSIDE the Pantheon before it closes for the day), and include a stop at Giolitti for gelato (it's kind of between the Piazza del Panthen and the Trevi Fountain).

As far as I understand, you can't actually visit the gondola repair place in Venice, but you can see one. It's next to the Church of San Trovaso, along the (narrow) Rio San Trovaso, just north of the Zattere.

I want to second the votes for climbing to the top of the Duomo in Florence for a kids' activity. (the dome is a double shell and is amazing inside, plus the view from the lantern at the top is magnificent) The book, Brunelleschi's Dome, is a bit much for them, but you could read it and explain. There's lots about the competitions for major art works in Florence that is interesting.

I agree that the Uffizi is a hard place to enjoy, even for adults, because of the crowds and the poor job they have done hanging the art with little explanation of why things are grouped together, or what you are seeing.

And Lucca's walls are cool to walk or bike, looking down into the town or out across the grassy fields surrounding the walls. As is the central Piazza, which is oval in shape, built on the site of an ancient Roman amphitheater.

My grandkids liked the cat sanctuary in Rome, too. It's too bad you are not staying there longer.