Tour or self Guided?

We took a similar trip from nice to Milan to Venice a little over a year ago, traveling by train the whole while on a self guided tour. I have also taken professional tours of Italy in the past. For Venice, if you really have no time or desire to do any research, I would book a tour, if only because the food and drink in the city is punch-in-the-gut expensive for the unprepared (I speak from experience. Dinner for two - one course - would set us back 80 euro. A beer in a bar - sitting or not - is 12 euro.) when I to do it again, I will spend more time consulting my tour guides for restaurant recommendations and grocery store locations. I would also recommend the professional tour if you plan to have a lot of baggage, need help getting around, or if you would prefer lodgings with the usual comforts of American/Canadian hotels. But, otherwise, for expense and experience I would do the self guided tour. The tourist office in venice, just outside of the train station, had very long lines,but was well worth the 30 min wait for the amount of help and information it provided. You may even be able to buy your train ticket to milan through them. The train system in Italy is very easy to use and you don't need to buy your tickets well in advance - we found that purchasing our tickets a day ahead at the train station was sufficient. We booked all of our lodging in italy through booking.com, which offered a ton of hotel options at good prices, with the ability to search by neighborhood. (Hotels.com is also very good. I like these sites because they do not charge you until you check out of the hotel, making cancellation easy.) We were never disappointed. In Venice,we stayed in the Cannaregio neighborhood, at the Hotel al Vagon, which was small but clean and comfortable, for 130 euro/ night and our room had a canal view. We were five minutes from the rialto and ten at most from san marco and there was a vaporetto stop very close by.

Fly back to Canada from Milan, or another final city. This is what the industry calls an open-jaws ticket, also known as multi-city on the travel sites. It probably will save you both time and money over returning to where you first landed. A quick test (on Orbitz) showed open-jaws tickets in Feb. costing about $30 extra but you save the cost of getting to Zurich where you would have to stay overnight. Making these arrangements will take time but so will shopping for a tour that suits you. An agent could tailor the trip, but at a price. D.I.Y. has always been cheaper for me, aside from certain day-trips.
By the way, I don't see the Austrian place listed in your schedule.

You're itinerary is kind of working against the grain. I see that Dornbirn, Austria is the far western city in Austria, on the Germany, Liechtenstein and Swiss border. Traveling thru the Alps this time of the year can be hit and miss because of the weather. You might want to take a train over to Innsbruck. Then, you'd go south thru the Brenner Pass and down to Venice. From Venice, getting to Milan is easy by train. I too say you should fly home from Milan open jaw'd. We about froze our tails off in Venice in February. The tides were high, and wooden walkways installed to get across St. Marks Square. You would have to make your own arrangements, as this is just not a time of the year that tours are often running.

If you haven't already booked your air travel, be sure to book an "open jaw" ticket, called "multi-city" on web sites like Kayak and Orbitz. This means flying into your first city (like Vienna) and out of your last city (like Milan). It is not always more expensive than a simple round trip, and even if it is, you save time and money by getting to where you really want to be and by not backtracking. Are you flying to Zurich because you want or need to be in Switzerland, or because it's "cheaper" than flying to Italy and/or Austria? If the former, fine (but still use open jaws for your return leg, to avoid backtracking to Zurich). But if the latter, remember that Switzerland is very expensive, so any money you "save" by flying to Zurich will be used up once there.

Thank you for all of your replies. We had considered "open jaw" but our arrangements changed and we now wish to return to Austria to visit our friends again before we fly back to Canada, and after our brief Italian vacation.

There is a good connection from Dornbirn to Venice with a change at Innsbruck, its still an 8+ hour journey, maybe the weather will be clear and you'll get some nice alpine scenery. My preference is DIY, but then I love planning. Carnival in Venice will end Feb 12, so hotel prices will be going down after that date (unless, of course, you want to do Carnival. Then get there before that date). Excepting Carnival, Venice won't have the major crowds of summer, but there will still be plenty of tourists there. I kind of like it then. In Milan, consider staying in the Navigli neighborhood, bit of a hipster-student area that your daughter might appreciate. There are several direct trains to Zurich from Milan 3.7 hour ride.