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Please note that a “Full Swiss Fare Card” doesn’t exist, you have a “Swiss Travel Pass”.
Both offers, Swiss Travel Pass (STP) and Swiss Half Fare Card (SHFC), include a Family Card. Your children will travel free of charge, but don’t forget to indicates their names and dates of birth when you order the STP or SHFC.
With the SHFC you have always 50% discount for the mountain excursions, with the STP sometimes only 25%.
You could also consider the Berner Oberland Pass for mountain excursions, but look carefully at the area of validity and if you have free travel or only discounts:
https://www.berneseoberlandpass.ch/public-transport/