We took a one and three year old to Switzerland for 4 weeks, and this is my cheat sheet for other parents travelling with young kids in Switzerland. It's based on my own experience and possibly-inaccurate deduction.
Here's our Swiss tourism wishlist map. We certainly didn't do all of this, but we still covered quite a bit.
Public Transport: Stroller friendly? Yes
The trains usually have stroller cars, luggage cars, and bike cars, marked with icons on the doors. The problem is knowing where to stand on the platform: we found ourselves running back and forwards across a long platform a few times. AFAICT the stroller car tends to be towards one end of the train, but it can be either. Train platform signs look like this:
A, B, C refers to areas marked on the platform. This train has 1st and 2nd class (2nd, 1st, 2nd) cars that will pull up to the B section, so that's where you need to stand. 1st and 2nd class are marked with 1 and 2 on the cars, and 1st class also has a yellow line running across the car (sometimes only part of a car will be 1st class).
Dear SBB: it would be great if the sign above also marked the location of stroller/bike/luggage cars. We were never the only people madly pushing a stroller around the platform.
We had no trouble getting our double side-by-side McLaren through the train doors of the stroller/luggage/bike cars (they all seemed pretty similar).
Trams are a little more tricky, some are stroller friendly, some aren't. To avoid a last-minute panicked stroller-collapse and kid-grab, look for the wheelchair symbol on the platform display:
If it's there, part of the train (sometimes the end, sometimes the middle) will be at the level of the platform and you can wheel right on. Again, the double side-by-side McLaren fitted easily. Once you're on a stroller friendly tram you will be able to wheel off at any station.
If the disabled sign isn't there it means all the carriages have steps and a metal hand rail in the middle, so you definitely need to collapse the stroller, which is sometimes better than waiting.
Public Transport: Half Fare Card
We bought ours from Zurich HB (on a Sunday, the train station is just about the only thing open on Sundays), and it cost 120 CHF, which sounds exorbitant, until you see the price of long distance train travel. There's a rather bewildering array of Swiss travel card options, and note there's also a SBB half fare card which is for locals and requires a passport photo and is more expensive. All you need for the tourist version is a passport or drivers license. Note that the "card" (it's a paper ticket) is tied to your ID, so unless you want to carry your passport everywhere, you should ask the SBB office to photocopy it for you and carry that, or use ID that you will carry around all the time.
We almost made our money back just doing two return trips from Zurich to Lucerne, but definitely made it back after doing some of the expensive tourist rail trips (like Grindelwald to Jungfraujoch, which was 170 CHF full price return) and riding lots of gondolas to the top of mountains.
We also got pretty good value out of the Saas Fee Citizens Passport, but that's only because we spent quite a bit of time there.
Playgrounds
A few restaurants with outdoor terraces also had playgrounds attached in the alpine resort towns, at which we threw money for a meal with adult conversation and quiet kids.
A number of gondola routes in the mountains have excellent playgrounds with mindblowing views at halfway stations: Kreuzboden, Winteregg, and Bort in particular.
Restaurants
Are expensive. We mostly rented places with kitchens and cooked for ourselves. Migros and Coop are the major supermarkets, don't try to find alcohol in Migros.
Minimum Age for Tickets
The one exception to this rule seems to be accommodation. It seems to be relatively common to have a base rate, then pile on charges per-person (tourist taxes, cleaning etc.) which apply no matter how old that person might be. Watch out for this on VRBO, where it is very difficult to accurately price compare, or sort by price, due to all these hidden charges.
Car Hire
So we hired a VW touran automatic for 12 days for about 1000CHF, which was pretty reasonable. Great car: enough room for all our stuff, LATCH mounts for car seats, and even enough space for an adult to sit between the two carseats comfortably. Better than what we have at home! For some reason it was about 200CHF cheaper to pick it up at the airport, so I took a train ride out there. The car comes with a motorway toll sticker.
The roads are excellent, signposting is good, and we had no trouble with using Google maps for navigation, even in the more remote country areas.