You don't mention whether you've traveled internationally with your kids before, so please feel free to ignore me these are things you already know :)
We only have one kiddo (just turned 5), but we've done three international trips with him so far, and we're planning to be in Italy for two months this summer. I'd strongly encourage you to "home base" as much as possible. Packing up, changing locations, getting to a new place, and unpacking eats up a lot of time, and every time you change locations is an opportunity for someone to leave behind a favorite toy or stuffy (100% speaking from experience haha). I would home base in Venice, Florence, and Rome, keeping in mind that it will be hot and you probably will be limited to one "major" site a day, so spending a week in those cities still might not allow you to see everything on your list. Then you could add a few days at the beginning in Milan, or head straight from Milan to Lake Como for a few days of jet lag recovery before moving on to Milan.
YouTube has a lot of interesting "travel for kids" type videos, with kid-friendly information on everything from specific cities, to typical foods, to art pieces. We've been watching Leonardo da Vinci and Venice videos in preparation for our upcoming trip. This helps my kiddo get a "preview" of where we're going so he has some time before arrival to absorb some of the info.
One other thing we've done before that is super helpful is to stay at the Hilton hotel that's connected to Rome Fiumicino airport the night before our flight. Some people might consider this a "wasted" night, but it's so much less stressful for us to just be able to get up and walk to our gate, rather than relying on transportation. Our kiddo also likes getting to walk around the airport terminal, so it's still a fun evening for him.
Of course, my most important tip for traveling with kids is to PACK LIGHT. Truly, you truly do not need everything you think you do, even with kids. Plan to bring just the essentials, then realize that you can go out and buy almost anything you need. Especially if you're using public transportation, you will not want to be hauling 5 suitcases on and off trains or buses or vaporetti, and the younger kids will not be able to manage their own belongings.
And above all - have such a fun trip!