We are traveling from Verona to Zermatt on Sunday, July 23rd, then from Zermatt to Murren on July 26th, then from Murren to Zurich on July 30th. Any recommendations on renting a car for the whole duration, or just for parts? So far, I have had no luck finding a train from Verona to Zermatt on 7/23 (maybe because it is a Sunday? or does not go to Zermatt?). I have heard that you cannot drive a car in certain parts of Switzerland. We are also open to hiring a driver to transport us part of the way. So any advice would be much appreciated (including particular companies you might recommend).
So far, I have had no luck finding a train from Verona to Zermatt
Where are you looking for them? I see several at www.sbb.ch
From Verona, you need to go to Milan to get a train into Switzerland. For Mürren, you have a choice between going via Luzern or Brig, for the fastest route. Or take one of the slower routes that avoids the long deep tunnels, if you aren’t in a hurry. You still need to start in Milan.
A car makes no sense for your plans, as both Zermatt and Mürren are car-free villages. Plus if you rent the car in Italy you will have a hefty drop fee if you leave it in Switzerland. And you would need to buy a Swiss vignette to use certain roads.
I count 6 connections between Verona and Zermatt on 7/23, 9:32, 9:50, 12:02, 13:02, 15:02, 16:32. Takes about 6 hours.
What are your plans in Zermatt and Mürren?
If those plans involve (quite probably) taking mountain railways and cable cars look in to getting the Half Fare Card, which gives you 50% off on all transports. This will also reduce the price of your Verona - Zermatt ticket.
If you rent a car you will only use it three times, to drive it from one car park to another, along routes where trains are faster..