Car rental or train travel ? How to decide?

Go to viamichelin.com, enter your point to point destinations and you'll get an estimate of time, tolls and fuel costs. Personally, I'd visit Luzerne and skip Zurich.

Edit: you'll also have to consider cost of parking which can be quite expensive. The road permit fee of 40 fr. Will not be charged since the car you rent will have this.

Driving on the highways in Switzerland is easy enough, but when you exit parking is expensive and can be challenging, including overnight if you choose a garage. Geneva, Lausanne, Bern and Zurich are cities which are not ideal for driving or parking.

Since your son lives here, does he already have the 1/2 fare card? At a cost of 120chf per adult for one month, the 1/2 far card allows you to pay 50% off most of the standard train, boat and bus fares in Switzerland. If you took the train to Lausanne from Geneva with the half fare card, it would be about 22chf per person round trip. If you had the 1/2 far card, it also allows you to purchase the supersaver tickets which are even less if you plan slightly ahead.

There is also a car share called Mobility and if you decide a car may suit a day trip, this may be an option to explore. If your son has a drivers license and a Migros card, they offer a free trial for membership and you just pay by the hour.

https://www.mobility.ch/en/private-customers/

Even if you think the One-Month Half-Fare Card is just breaking even on the train rides that you summarized, you probably haven't calculated the additional savings it would offer on any mountain lifts (expensive), lake boats, or city transport that you might use. A car doesn't get you to all the places that the lifts do. You are also in the country for an additional 11 days, during which you could continue to benefit from the Half-Fare Card.

All of the places you're visiting are well served by the excellent public transit network in Switzerland, and as Laura mentioned a car will not get you to all locations. You'll have to also include expensive fuel and parking costs and driving in congested cities, none of which are pleasant.

Also, visiting six locations in a four day time frame seems a bit "ambitious".

Since you will be there for 2 weeks, the Half Fare Card will also cover urban transit in Geneva. As mentioned, your son is likely to have a Half Fare Card already, if he is person 3 of this trip. You will also be likely using urban transit in Lausanne, Bern, and Zurich. Hate to see you go to Interlaken and not go as far as Lauterbrunnen and Muerren. Ditto substitute Luzern for Zurich.

I like driving and driving in Switzerland is easy peazy.

You can see a lot more of the country by driving. Trains are nice but you only "glimpse" the passing scenery and cities. Yes, parking is a challenge unless you line it up before you go at your hotels.

Here is an example. We stopped in Basel and could have taken transportation to Montreux then to Interlachen and Lucerne. We drove, stopped in Friborg, Gruyere (very cool place), Gstaad, stopped for picnic in Alps and for an hour or two drank wine and ate cheese watched the parasailers jump off cliffs! Then we drove up to Grindelwald and had lunch, went to Tasch and up to Zermatt and saw the Matterhorn, then on to Lucerne. Took three days. You can't do that on a train!!!!!!

Do not miss Lucerne. you are hitting all the main towns except Lucerne. I recommend it .