Travelling most of the time by car to a region you want to explore using cable cars, mountain trains, etc. indeed makes the Swiss Half Fare Card
the option of first choice.
As you can see this card is valid during one month, will cost CHF 99 per person and will give you a 50% discount on travelling by train (1st or 2nd class), bus and boat, as well as a 50% discount on most gondolas, funiculars and mountain trains. Your children will travel for free with the (free) STS Family Card.
In case you want to travel for free on one day you can purchase an additional daycard ("Tageskarte zum Halbtax").
If, on the other hand, you would like to be able to travel for free on some days during your stay, please look into the possibilities of the Swiss Flexi Pass
. This Pass also has a validity of one month but gives you a 50% discount and free travelling for 3, 4, 5 or 6 days of your choice within this period. Purchasing this Pass for two persons travelling together will give you a 15 % discount and is called the Swiss Saver Flexi Pass
. With the additional (free) STS Family Card your children will travel for free.
I just want to mention this second possibility because the Swiss transportation system is very well organised and convenient. Travelling by train (bus, boat) gives you the opportunity to see different landscapes in a very relaxing way.
Many trips can be planned using the Timetable Switzerland
Here are suggestions for hikes
in the Bernese Oberland, but you can also find hikes and daytrips in Wallis and Graubünden (but maybe that's too far away?)
I wish you and your family a very pleasant stay in Switzerland.