Have you actually looked at prices for Switzerland? I'm imagining the shock in your eyes once the bill comes for your sit-down meal for 5. Unless the sky is the limit, I suggest you look into a Germany/Austria visit instead.
Both countries - especially Germany - offer heavily-discounted day passes for 5 persons traveling together.
https://www.bahn.com/en/view/offers/regional/regional-day-tickets.shtml
For your focus area, click on Bavaria and Baden-Württemberg (the two most southerly German states) using the map at the page above.
Baden-Württemberg is home to some great places, including the Black Forest...
Gutach:
https://www.tripadvisor.com/Attraction_Review-g1825958-d190955-Reviews-Schwarzwalder_Freilichtmuseum_Vogtsbauernhof-Gutach_im_Schwarzwald_Baden_Wurttemb.html
https://www.tripadvisor.com/Attraction_Review-g1825958-d2657528-Reviews-Sommerrodelbahn_Gutach-Gutach_im_Schwarzwald_Baden_Wurttemberg.html
Gengenbach:
https://www.pfeffermuehle-gengenbach.de/files/gengenbach-innenstadt.jpg
Schiltach:
https://www.orte-bw.de/grafik/uploads/12503_2010_1040.JPG
The scenic Black Forest Railway bisects the Black Forest on its way from Offenburg (near Strasbourg, FR) to Lake Constance (Swiss Border area.) Gengenbach and Gutach are just two of several nice stops on this route:
https://www.black-forest-travel.com/places-of-interest/black-forest-railway.html
You want to stay in a limited number of places; Gengenbach makes for a good base town in the Black Forest as its just a few miles from Gutach and enables guests to make easy day trips by train to Schiltach, Strasbourg FR, Freiburg, and other places on/near the Black Forest Railway. A stay of 4 nights there would not be too many.
A big plus of visiting the Black Forest is that your whole family can use the trains for free throughout the BF provided that you stay in "KONUS" towns (where guests get a KONUS ticket for rail travel for their entire stay.) Gengenbach is one of those many towns.
https://www.youtube.com/watch?v=KkgzMXQ7blQ
If you split your time into 3 base towns, then two more stays, one in Bavaria and another in Austria, would make for a nice visit. I suggest you look into Mittenwald for Bavaria and perhaps Werfen or some other nice place near Salzburg.
Mittenwald - mountain lifts, nature, near Oberammergau,Garmisch and Innsbruck Austria for day trips:
https://hastingshouse.typepad.com/hastings_house_us/2007/04/mittenwald_germ.html
Werfen (Hohenwerfen Castle w/ falconry show, Eisriesenwelt ice cave experience, Sound of Music Trail, day trip to Salzburg?)
https://www.salzburg-burgen.at/en/hohenwerfen-castle/
https://www.eisriesenwelt.at/en.html