Spring Switzerland loop

This is a nice loop, except for one point, I would skip Zürich and go direct from the airport to your first location (Bern).
Why Baveno? I assume you have your reasons. Look up routes and travel times on https://www.viamichelin.com/ and then add 20-50% because you will be stopping en route.

Biggest problem is a car is not much use in cities (Bern, Luzern, Montreux). You can't drive in the city centres, you have to park (pay) on the edge of the centre. Do not assume hotels have parking, always check. Zermatt is car-free, you cannot drive there. The nearest is Täsch, where you park (pay) and take a train to Zermatt.

I would recommend any time from mid-May onwards. March and April are between seasons, between the winter Ski season and the summer season.

If you are driving to Baveno (very nice, I love the gardens on the islands and Maggiore is a lovely lake) in Spring and early Summer, what route will you expect to use?

It is by far the outlier of your journey, especially when the passes are closed because of accumulated snow. So you have to do a lot of around the sun to get to the moon.

I did this in April in my own car which I drive from England every year. The sort of direct route is Brig over the Simplon Pass. Very steep, very winding, just my sort of high mountain driving. The pass had just opened and at times I had walls of snow on the side of the road 20 or 30 feet high. The road was wet most of the way, and the journey is quite slow. Alternatively you can put your car on one of the trains to Isole, and then it is just downhill to Domodosola and then into Baveno. That train is not cheap and you need to ensure that it is going on the day and day you need.

All the different places you list can be very easily linked by frequent and often very scenic trains - no worry about winter driving in the mountains. It would be faster, stress free, much more scenic, especially for the driver, and hassle free.

Many thanks for your replies. I believe we will do trains and not the car. We can start the trip around June 1 or so no problem. Curious why to skip Zurich? Just better scenic options I suppose. Any trip suggestions you all can give would be appreciated. We love mountain scenery, lakes and rivers, beautiful villages, gardens, etc. Thank you!

Weather can be all over the place in spring. Last year (2018) it was very warm and sunny. This year it snowed several inches when we were in Lucerne on May 4, and the whole month of May was chilly (we went into northern Italy and they had the worst May in 50-something years, but my daughter who lives there says the Lucerne area was horrible--rainy and cold). I hear the weather still hasn't been great in Switzerland, but next week it's supposed to be 35 C.