Mürren is in Switzerland. It is a car-free alpine village in the Berner Oberland, one most popular places in Switzerland with members of this forum. It is perched high above the Lauterbrunnen Valley, a which looks a lot like Yosemite. Just getting there is an adventure, involving not only trains but a cablecar. Most people who visit there or elsewhere in Switzerland buy a travel pass to cover the trains, boats, and other transport**—-but the kids under 16 will all ride everything for free, as long as the parents have a travel pass.
**Trains and boats that provide transport to cities, towns and villages are covered with a Swiss Travel Pass, but not the recreational cablecars and gondolas that serve as ski lifts in winter and sightseeing rides in summer. Most of those are, however, covered with a special pass for the Berner Oberland area.
Here is a blog with photos and information about the village:
https://www.swissasap.com/stories/blogs/murren-to-gimmelwald/
And here are two of Rick’s travel videos on the area and the villages:
https://www.ricksteves.com/watch-read-listen/video/tv-show/swiss-alps
https://www.ricksteves.com/watch-read-listen/video/tv-show/best-of-the-alps
I believe the lower one, from 2003, has fottage of the local Mürren festival and parade that takes place the first Saturday in August. We have been there for the parade several times, and accidentally ended up a part of it once!
Switzerland as a whole is very family-friendly, well beyond the free travel for kids. The playgrounds are particularly nice. We have taken our grandchildren there twice now (both times to Mürren), when they were 6 years old and again at age 11. They are again clamoring to go back.
Here are a photo and information about the “Flower Park” playground just above Mürren. You can reach it by walking up, or riding the little funicular which goes up and down every 15 minutes or so. You can see this from the balcony of the apartments I mentioned.
https://swissfamilyfun.com/allmendhubel-flower-park-playground/
On the opposite side of the Valley, above the village of Wengen, is another fantastic playground, this one with slack lines and other activities for older children as well as the usual things for smaller children.
https://www.maennlichen.ch/en/summer/experiences/alpine-herdsmans-playground.html
Just over the ridge from Wengen lies the larger village of Griindelwald, which offers an array of adventures including ziplines, mountain coasters and Trottibikes from the First gondola, and a Rodelbahn (summer luge) at the Pfingstegg lift. Note that some of the activities offered at the First lift have height, weight or age requirements so may not be available to the 2 younger children.
https://www.jungfrau.ch/en-gb/grindelwaldfirst/
https://www.pfingstegg.ch/index.php/en/activities/toboggan
These cablecars and gondolas are free for adults as well as children if you get the local travel pass, the Berner Oberland Pass (activities like zip line etc. cost extra).
Boat rides on the nearby lakes, Thunersee and Brienzersee, are also free with a pass, and you can use the boat to visit a local castle. Or you can take a boat (or train) to Brienzersee for the Ballenberg open-air museum, very popular with families.
https://schlossthun.ch/en/
https://ballenberg.ch/en/
Towns and cities like Bern (the capitol of Switzerland) and Luzern are close enough for a nice daytrip.
The 6-person, 3 bdr. Apartment we like so much is Chalet Oberdorf on this page:
https://www.topapartments.ch/en/6-persons
It is also listed on AirBnB (where we rented it) with a lot more photos, under the title “Chalet Oberdorf—-the Perfect Mürren location”. I cannot post a link because I have the AirBnB app and my device defaults to that. But you can google it.
Just downstairs, in the same building, is Chalet Oberdorf B
https://www.topapartments.ch/en/4-persons