Initial post was to make sure I was thinking logically in regards to location. Greater details on time spent when and where were to follow once I could confirm that these two locations make sense. Sounds like in theory they do.
Let me provide a bit more detail as to what we are looking for. Ideally, 12 days total inclusive of flights and movement around. My wife struggles as does my child to move around a lot, and as most seasoned travelers will agree, that is more beneficial than not.
My feedback from friends that have gone to Rome are crowds, grungy city, not always friendly (not so worried about this as it could be situational). For me personally, travel is about history, food, culture, local experiences, architecture, beauty, etc. Rome surely has so much history and that is a big part of why we would want to go.
The typical sites in Rome are to be expected; What about off the beaten path or special experiences anyone has had there?
Vatican would be extremely important to us and I understand private tour is the way to go here. Would love recommendations on guides. We stay in higher end places, love great meals (does not have to be high end to be great) but love a fine dining experience a few times on the trip.
Regarding Sardinia, I have not spent much time researching but know it is a vast island with various sites and activities. Would want to get close to the food scene, beaches, boating, any history, local towns worth seeing.
There is never enough time on any of these trips and If I could spend weeks at a time away, would love to do so. I think the best strategy for us would be 3 nights in Rome and 8-9 nights in Sardinia. Not going to see everything but makes you want to return back if you fall in love.