We did Italy last summer with kids ages 11 and 13 and loved. My kids want to become Italian and live there forever
I have to say that Rome was not all that. We loved Venice and Amalfi esp Positano.
Venice for 2-3 days is enough for sure and only 4 hours by speed train from Rome, easy. If I did it again, I would actually skip Rome but if first time, I would only do 2-3 days there as well. I would look at other places you can go either as day trips from Rome or just other towns and travel via train throughout.
Amalfi is amazing. Boat rides is where it's at esp for older kids. It's hard because it's the opposite direction from Venice but what we did was Rome and Venice then 5 days down south before heading back up a day to depart from Rome.
I looked at hitting Orvieto and Ponza day trips from Rome - I couldn't make it work unfortunately with our schedule. Another option is to hit the islands of Italy which a lot of people don't realize is amazing. So Capri, Ponza, Ischia.
For us, Italy is about taking your breath away in it's beautiful sights. The water and the way their architecture is of small towns. It's about food. It's less about hitting 101 museums and actual seeing stuff as it is enjoying our environment. We did Pompeii and we did Colosseum but honestly, we loved it for the former experiences even more!!