The trip I’m taking to Italy is a private tour, just for three of us with our own tour guides. Rome, Amalfi Coast and Venice. We are obviously paying a premium for the private tour. Are we expected to tip our tour guides and drivers on top of the cost of the trip?
I would not
You have agreed on a price already
https://community.ricksteves.com/travel-forum/italy/tipping-4072a22d-cee5-4ed0-8f8d-778323398bc7
We are obviously paying a premium for the private tour
Why would you want to give them even more? They have charged what they think the job is worth.
Would you tip the people on the supermarket check out?
Here's a current thread on tipping in Italy.
I feel that if I'm already paying an exorbitant price (in my estimation) I wouldn't. Case in point last April having a husband/wife driver & guide cart 4 of us around the Amalfi Coast for 6 hours, pickup/dropoff was in Salerno...price was $400. Had to do it to get around to Vietri sul Mare, then Ravello, then Minori. No tip there. And that was through a friend...
Conversely, earlier that trip, we took a private excursion from a company that started at a designated spot in Florence, a young lady picked us up, took us to a castle/winery in Rignano sull' Arno, we sampled the goods and bought some, then she drove us to her parents' house in the Chianti hills--just beautiful--and her mom showed us how to make pasta, and we had a charming lunch--that was all over an 6-7 hour period. Price I believe was $570, not bad for 4 of us. After the young lady drove us back to Florence, we each gave her 20 Euro as a tip. She was great, told stories, and I had a feeling that she personally wasn't going to get a high percentage of that original total price.
So it depends...