I live in Switzerland....
I realize that I'm a little late responding to this thread, but I live in Switzerland. Switzerland is very family friendly. You can find playgrounds in many spots and you can also stay in a kinder hotel that has kid's clubs, maybe for kids that are older than yours, though. It is stroller friendly in many spots. It is, however, not cheap. Plan on spending about 100-150 CHF for a family the size of yours for each meal. Try booking.com for apartments or hotels where breakfast are included. The grocery stores have prepared sandwiches for picnic lunches if you want to save a buck or two. Then it is just dinner out.
I would skip Zurich in favor of Luzern or Bern. They are both much prettier with more to do. If you have a chance, go to Montreux on Lac Leman (Lake Geneva). You will think you dreamed this place up, it is that gorgeous. Gruyere is fun to visit cheese and chocolate factories and is a short hop from Montreux. Lugano, Switzerland is pretty darn wonderful, too.
I, personally, think that Milan is totally skipable in favor of Venice or Florence. The Lake Como region of Italy is beautiful. Trains in Italy are easy.
I don't know much about the area that you are going to but it looks lovely, too. If you get a chance to go to Krystalwelten Swarovski near Innsbruck, Austria, go there! It is facinating.
I live in Basel which is a great place, but alas, skippable on a vacation.
If I can help in any other way, let me know! Cheers!