Suggest a circular route.
Geneva: 1 night
Interlaken: 3 nights Option to take the slower scenic route via Montreux and Zweisimmen
Luzern: 2 nights
Varenna: 3 nights via Thalwil, Chur, St Moritz, Tirano. This is a 9 hour journey over the scenic Bernina Pass. Option to spend a night in St Moritz to break up the trip.
Milan: 2 nights
Zermatt: 3 nights
Geneva to fly home
That is 14 nights and should be doable. Consider a 15-day Swiss pass at 458 CHF and all local transport in Switzerland will be included except mountain lift excursions which you will get a discount with the pass. Less expensive would be to get the 30-day Half Fare card for 120 CHF, then everything will be 50% discount but you will have to buy tickets for each journey. Buy Italian train tickets as you need them, they are not expensive.
As an alternative to Interlaken, consider staying in lauterbrunnen, Muerren, or Wengen. Worth it to be in the mountains rather than near the mountains.