I think you need to decide what your goals are for the trip, before deciding which one to take. If you want to get the full flavor and essence of what people think of when they think of Italy, I would go with Viva Italia. Also, I would take into consideration if you have been to Italy before or plan to go back in the future. If this is going to be your only trip to Italy, I think it would be a shame to miss David in Florence and the magic and mystery of Venice. My kids loved it. Tuscany was awesome too. There is so much history that surrounds you on the Viva Italia tour. My 2 older kids had studied Rome at school, so they loved seeing all the things they had studied come to life in front of them.
On the flip side, the Amalfi coast was breathtakingly beautiful. It sounds like once you get to Sorrento and the coast ,it is a much more laid back trip than the Viva Italia trip, which can be a plus with kids. My kids loved playing in the surf on the Amalfi caost and collecting sea glass. It sounds like that Amalfi coast trip is a more relaxing trip . We spent three days on the Amalfi coast. I think that was just about right, maybe a day more to have more time to wander through the shops a little more.
We initially flew into Milan and took a flight from Milan to Naples. We then took a shuttle to the train station and made our way to Sorrento. While we were on the Amalfi coast , we hired a driver who took us around. On the last day he took us back up to Rome.
My kids had a fabulous time on the Viva Italia tour. In fact, my 5 year old cried on the last day he was so sad it was over. One tip that might be helpful for those with kids, is to maybe let the kids sit at their own table with other kids rather than sitting with just your family. We had 7 in our party so we frequently were at a table with just our family. We ran into one of the other families one night at dinner on our own and invited them to join us. The kids sat at one table and the adults at another. The kids had much more fun, once they got to know some of the other kids. They can't wait to go on another
ABD adventure.
Hope that helps.