Coming from the US with only 8 nights in Europe, and with young children - two cities MAX, or you'll be sorry.
As said, you don't know how jet lag will hit, but it's best to assume your first day will be a jet lagged haze, at least for some in your family if not all. The last day is taken up with getting to the airport. When trip planning, it's best to count nights, and remember that while two nights equals one full day, one night is less than a full day of sightseeing.
Part of what makes longer stays better is that you don't have to be "busy" all the time. You can focus on one or two major sights per day, rather than running around to try to see "everything." People who have short visits to Venice and Rome often don't enjoy them.
Plus, by sticking to one country, you'll have less adjustment in things like language and menus (even more important for your kids than for the adults). You can all start to learn some basic Italian, which will enhance your trip. And, you'll save money by not taking so many trains or planes.
So, I'd see Venice and Rome on this trip. Again, you won't feel "shortchanged."
Do look into flight connections carefully. Many flights from Venice to the US connect in Europe, and these can leave at shockingly early hours. Getting to the Venice airport for an early flight can be expensive (over €100 for a water taxi) or time-consuming (1-1.5 hours for vaporetto - water bus - followed by land bus). Rome has more late options for flights back to the US. But even if you have an early flight, a taxi ride to the airport takes 35 minutes and costs €48. Plus, many find Venice easier to adjust to than Rome. So, you'll probably want to see Venice first, then train to Rome (less than 4 hours), then fly home from Rome.