Feedback on my itinerary

Are you planning to see the Palatine Hill and Forum along with the Colosseum in Rome? A lot of the entry tickets include that and give you admission for 2 days.

Also, if your younger son likes catacombs, consider this tour: https://theromanguy.com/tours/italy/rome/catacombs-bone-crypts-tour To be honest, I found the Capuchin Crypts FAR more interesting than the catacombs. (Unlike the ones in Paris, the bones have been removed from the areas open to tourists.) But the tour is a nice combination and includes a stop at the Appian Way where there are original stones on the road.

In Venice, in your "wandering" include a ride on a vaporetto down the Grand Canal.

Adding: if you want to skip the Catacombs, due to time and energy constraints, I'd still suggest the Capuchin Crypts. They are at once both creepy and beautiful. My husband said the skeletons in robes made him think of Dementors. I'm guessing your boys would find this site fascinating.

Possibilities while in Rome: go out to Ostia Antica (Rick has a walking tour in the free Rick Steves Europe app), walk part of the Appian Way, and atop by the cat sanctuary at Torre Argentina.

Week one: Saturday: Piazza del Popolo Rome’s oldest square is worth a visit; don’t forget your camera.
Week two: Venice: take a vaporetto (water bus) from one end to the other i.e., the train station to San Marco Square at twilight. This way you’ll be able to voyeur inside the illuminated foyers of the baroque palaces along the Grand Canal and not notice the decay on the exterior. The experience took me back in time.

That looks like a very fun and well-paced trip that will give you plenty of time to explore and catch your breath between blockbuster sights. Your guys are lucky to be able to travel this way, and you're smart to include their interests in your plan. Most people would try to fit Florence in, but if art isn't your big interest you're better off focusing your time elsewhere. (Not that there isn't plenty of art in Rome and Venice....)

Venice Get tickets to the Secret Itineraries Tour at the Doge's Palace. It's really interesting and all about history. The rest of the palace is art and architecture. It will be hot during the tour - get the earliest time slot and take cold water and a fan. Row Venice has gotten good feedback here. It sounds like something every kid would love, adults as well. It's well worth visiting the museum of St Mark's, not so much for the collections as for the close up views of some of the mosaics and balcony views of the interior and of St Mark's Square. The very best gelateria in Venice (so say the locals) is Suso, not far from Rialto Bridge, but tucked into a small side street off Campo S. Bortolomio.

Bologna The university tour is interesting.

The tour of the historic center offered by the Bologna Tourist Office in 2015 was good as well. I don't know whether they're running that tour now.