There are enough top-class sights in Switzerland and Italy to keep you occupied for months, probably years. You need to think about what sort of experiences you want during your trip: mountains (walking or looking?), beaches, historical museums, art museums, archaeological museums, natural history museums, palaces, Roman ruins, markets, walking tours, cooking classes, active sports, historical landmarks, etc.
Traveling in Switzerland is very, very expensive. For some us, that would mean less time in Switzerland and more in Italy.
Do you plan to rent a car? You'll need to drop it off in the same country where you picked it up unless you're prepared for an extremely high additional charge. For most itineraries, trains are sufficient when supplemented by the occasional bus or lake boat. I do not know about Liechtenstein.