Hi there, Welcome to the Forum. Well you couldn't drag me on this trip, but then again, we don't know your travel style, so more info about what you'd like to see & do (besides watching the scenery go by from the train) would be helpful.
Often people count their arrival and departure days, which really are wasted getting to and from, so is this just 12 days on the ground? Consider how you like to spend your time, have you been to Paris? I would probably spend 5 nights in Paris & 5 nights in Rome, (=10 days), if you haven't been to either, then work backwards with what time you have left and see how you could take a train trip between one or 2 others.
Have you booked flights yet and when is this trip? When are you traveling? Heat of summer would make this really painful! Why specifically Palermo, I think it would be amazing to go there, but by then you're likely to be exhausted, how about ending trip in Rome or Naples? IF you go to Switzerland, St Moritz isn't that attractive, stay in one of the villages on either side Sameden or Pontresina. Good luck!