train travel from Rome Italy to Munich Germany via Salzberg., Austria

Hi,
This is my second time to Europe - two years ago my wife and I did a 10 day trip from Zurich to Paris to London by train thru the Alps. It was fast but fun. Most of the time in the Alps was rainy and cloudy and we did not see much, in Interlaken and Lauterbrunnen. In May 2013, my wife and I wish to fly into Rome, Italy for a three day visit, then take a train to Venice, Italy for an overnight and morning. The next afternoon, we wish to take a train trip through the eastern Alps to Salzberg or Innsbruck Austria for one or two days stay. Then we wish to take a train to Munich for a two or three day visit in Munich alpine area. Then we will fly back to USA from Munich. Can this be done? The main things we wish to do is take a DAY trip through the Alps (with perhaps a short stop somewhere in the Alps), at least two days to visit Salzberg and/or Innsbruck, and three days to visit Munich and a couple of the Alpine walled villages near Munich, and at least two or three days in Rome, in addition, with a few hours in Venice to at least have time to take a canal boat ride. We have only about 12 days to do this and two of those days would be fly days to and from the US. Is this a possible itinerary? What would you do to get a quick overview of this beautiful area of Europe. Two years ago we spent three days in Lauterbrunnen SW and thoroughly enjoyed it, even though it rained or was cloudy most of the time while in the Alps. Would love to go back or at least to the Matterhorn area, but a train ride this spring thru the eastern alps would be sufficient. Thanks for helping me out with this.
Gregg Duckworth, Atlanta. Georgia