Road trip itinerary-Switzerland and Austria

You seem to be doing a LOT of driving, especially with two 6-year olds.
Drive time: Zurich to Salzburg - 4.5 hours
Salzburg to Vienna - 3 hours
Vienna to Innsbruck - 5 hours
Innsbruck to Zermatt - 8.5 hours
Zermatt to Montreux - 2 hours
Montreux to Gruyeres - 30 min.
Montreux to Lauterbrunnen - 2 hours
Lauterbrunnen to Lucerne - 1 hour
Lucerne to Zurich - 45 min.

Switzerland has practically the best train system in the world, plus kids ride free on it with their parents, so there's not a lot that would convince me to drive in Switzerland. Many of the double-decker Swiss trains have playgrounds on the top level, clean bathrooms, and kids can move around.

I would point you to this recent post about the hassles of driving in Salzburg: https://community.ricksteves.com/travel-forum/austria/didn-t-have-the-best-time-in-salzburg-but

If it were me, I'd pick 3-4 cities, max, and stay 3-4 nights in each of them. Otherwise you're going to wear yourself out and have some insane kids in the process. You're looking at driving 27 hours over 14 days, and that's if everything goes perfect, you don't get lost or run into traffic, etc.

Hi,
I have to agree with the above poster, this itinerary is too busy. Also, train is much better. I don't know what your priorities are, but with 14 nights I can suggest a "north-eastern" loop:
Land in Zürich
Innsbrück (3n), with a day trip or two - don't know the region too well
Vienna (3n), 2 nights can't do it justice and even 3 is tight
Salzburg (2n)
Füssen (2n), for Neuschwanstein castle
Luzern (4n), with daytrips on the lake, to Mount Rigi, and/or Pilatus

Or a "southern" loop
Land in Z
Lauterbrunnen (4n)
Gruyères area (2n) (I am just back from Montreux and found it entirely underwhelming, except Chillon castle)
Zermatt (2n)
Stresa or anywhere on Lake Maggiore (3n)
Luzern (3n)

I agree with the other poster -- you are moving around quite a bit and it will be exhausting. We would probably only be in four cities in this time frame. You won't need a car in Lauterbrunnen or Lucerne, but I think you would in Montreaux, esp. if you want a day trip to Gruyeres. However, with only one night in the area and using your day to be in Gruyeres, I'm not really sure why you need to go to the area for such a short time? Same thing with Zermatt, as the weather can block your view and you have a limited amount of time. However, if you do wind up going, I'd recommend the tour at Cailler Chocolate Factory near Broc, esp. with your kids -- there's scenery and puppeteering that reminded me a little of Mr. Rogers.

We didn't get to Austria on this trip, and were in Bavaria instead -- visiting the castles around Fussen and then into Munich. Fussen is pretty manageable from Innsbruck, but I can't tell you if it's worth the trade off instead of some of those other cities.

I agree with all the above, a lot of moving around, you would be spending too much time driving.
Plus, you can't drive in big cities like Vienna. You need to park (pay) and use public transport.
Similar for middle sized towns like Salzburg and Luzern. Most hotels will not have parking, and if they do it will cost.

And you can't drive to Zermatt (car-free), only way in or out is by train (or hike over a mountain☺)

Gimmelwald is also car-free (part of its attraction). It is a sub-village of Mürren (also car-free). You would need to leave your car at Lauterbrunnen. Do as a day trip from Lauterbrunnen.

"We land and depart Zurich at 10 a.m" I don't know where you are flying from, depending on that you would need to be at the airport 90 minutes to 3 hours before that. Allow 70 minutes by train from Luzern, longer if you need to hand in a hire car as well. You can do the arithmetic on that yourself.

Driving for nearly 5 hours after, I presume, an overflight flight, would be exceptionally dangerous - especially WITH KIDS IN THE CAR.

Please, take the train - for your safety and for the safety of others. Trains are also so much easier with kids.