There is a railway line following the east shore of Lake Como, Milano-Lecco-Varenna-Colico, than turns east to Sondrio and Tirano. At Tirano it connects with the Bernina Express. Another railway line starts in Milano, just skirts the lake at Como, goes on to Switzerland and Lugano and north to Gotthard and Zurich. If you look on a map you will discover the two lines diverge just north of Milan. To ride the Bernina express you need to access it through the east shore line; but if you are in Como or Lugano you are on the wrong railway line.

The last time I checked the timetables a day trip was possible from Milan only leaving with the earliest train at 6:00am or so, and staying just a couple of hours in St. Moritz. I guess leaving from Como or Lugano, that are on the wrong line, would turn out to be still lomger or too complex (for example ferrying to the east shore) so it should turn out to be too long for a day trip.

I don't think it would be easy. Would you have to take luggage on all these connections? Did you see this thread?

http://www.fodors.com/community/europe/train-from-tirano-to-colico-italy.cfm

Too much hassle and potential disaster.
See your mountains in the Dolomites which is on your route.

We don't have anything booked yet so we could really stay anywhere along the appropriate route. My original thought was to leave our bags at hotel in Verona where we had wanted to go. Then stay one night in St Moritz with just a small backpack . Then return to Verona before heading off to Venice. We will have cars but would prefer to dump them and take train. I couldn't figure out how to do that fromVerona so hence the idea to stay at one of the lakes instead. I have 4 kids on this journey and they are really excited to actually get to Switzerland . I know it seems like a hassle, it's just one of those crazy whims. At this point we will have been in Italy for 2 1/2 weeks and only have stayed in 3 so there will have had a relaxing pace. I appreciate your ideas.