Brian, we see so frequently that travelers have to see see everything you possibly can because you may never return. Then, they not only fly to Europe, they fly through it as well. Blink at the site, grab your luggage and run for the train. Some even plan several night train journeys to save every precious hour of daylight. Since that seems to be your plan, here's some more info.
1) Arrive Milan 8:00am. Arrive Milan Centrale train station about 10:30am. Buy your tickets to Venezia Santa Lucia at the self-service machine. This machine will prompt you in English, make your seat reservations and accept your American credit card. Catch the 11:05am ICPLus train to Venice. 3hrs to Venice. Cost for 4 - 88Euro. If you miss that train, there are 3 more by 12:05am. Arrival time is 2:05pm. As you come out of the Venice train station, I need a favor. Stand on the top of the stairs and take your first look at the Grand Canal. It's right in front of you. Your world will stop.
2)Venice to Florence. I suggest the 8:43am but there are several later trains. About 3hrs. Cost for 4 on the Eurostar is 129.20Euro. If you take the ICPlus train at 9:21am, the cost for 4 is 86Euro. Yes, the ICPLus train is less expensive than the Eurostar-category trains.
3) Florence to the CT. 3hrs to Vernazza. 61.20Euro for 4 on the ICPlus/Regionale trains.
4) Don't know where you want to go in the Tuscan hill towns. Siena, San Gimignano, Montepulciano, Volterra?
5) Siena to Rome (my guess). 4hrs. 88Euro for 4 on the ICPlus/Regionale. Could be a bus segment depending on the run you choose.
6) Rome to Positano. 2hrs. to Naples on Trenitalia. 144Euro for 4 on the Eurostar. 78Euro on the ICPlus. Then, 1.5hrs from Naples to Sorrento on Circumvesuviana and another hour by SITA bus to Positano. Not too expensive here.
7) Positano to Milan. About 10hrs. 292.80Euro for 4 on the Eurostar from Naples to Milan.