Linda, I'm not Rick. This forum is sponsored by Rick Steves, but the answers come from volunteers like me who just do it for fun.
It would probably be 7 days including travel time
As you are flying from the USA, you probably have an overnight flight, then you won't arrive in Zürich until day 2 of your 7 days, and you will have to cope with the time adjustment.
Is it possible to rent a car in Switzerland and leave it in Venice?
Yes, probably but very expensive. Doing a one-way rental to a different country has a large surcharge because somebody (a paid employee) has to drive it back. One way rental within the same country is usually minimal or no surcharge.
But we like the freedom of having a car to stop or detour where we want. Being from the SW part of the USA we aren't familiar with using train systems so not sure how much freedom there is to those as far as getting on and off and the places they go to.
At the risk of offending you, I guess you have said "Fly then rent a car" because that is what you always do, and it is the only option where you live. The places you have chosen are perfect for travelling by train, and NOT using a car.
It won't restrict where you can go, because cars can't drive up mountainsides, they can't go on lake boats and Venice is one place you definitely can't drive, unless the car floats ☺
So I suggest:
- Land, go direct to Luzern for 1-2 nights. Train from Zürich airport to Luzern takes 70 minutes, and runs twice per hour.
- Take train to the Jungfrau region.
- This is a scenic train line, the "Brünig line" (google it)
- Stay in Mürren or Wengen for 3-4 nights.
- For info and hotels see here: https://jungfrauregion.swiss/en/summer/
- These places cannot be reached by car, train only. (click here for photo). You can see down to Lauterbrunnen in the valley bottom, which is where the road ends. Note the waterfalls.
- Finally train to Venice. Long run, bring food and drink with you. Look out the Window as the scenery goes by, no traffic jams. Sip a little wine.
- The train arrival in Venice is one of my favourite scenes. You walk out the front of the station, and in front of you is Venice "main street", the Grand Canal. (click for Google streetview).
If you are train newbies, you need to climb a learning curve about trains.
Start here: https://www.seat61.com/Swiss-trains.htm
then here: https://www.seat61.com/international-trains/trains-from-Switzerland.htm#Switzerland-Italy
And when you have any specific questions, come back and ask.