Perche offered some sage advice upthread.

We spent almost 3 weeks in Italy last year, saw Sorrento and the surrounding area, Florence, Rome, and Venice - all "somewhat" in that we hit the high points only. We always strive to see more of less, but at points (cinque terre) we broke our own rule and the result was disappointing.

Italy is best seen slowly on foot rather than rapidly through a train window. You would do well to seriously trim your itinerary.