This isn't easy to figure out but I think you're on the right track by choosing just a pas for Switzerland. The 2-country passes are for first class only, so more expensive, and they don't fully cover some of the private railways in Switzerland (there is a supplement).
But I'm not sure the BO pass is the right one for you. First off, the "junior pass" and the "family card" both cover children UNDER 16, so the 2 older kids won't qualify. (The difference between junior card and family card is this: the Family Card and the Junior Card have the same coverage; there are just two different offers, because the Swiss Family Card is free of charge for people buying the Swiss Card, Swiss Pass or Half Fare card. Otherwise, you can buy the Junior Card for Sfr. 20. per child, up to 2 children. (This would apply to the BO regiopass---no Family Card available with this one).
TAlso, te BO regiopass won't get you TO the Bernese Oberland from France. So I am thinking that your best option might be a 3-day Flex pass for the adults and 2 older kids, with free Family cards for the 3 younger kids. This would cost 4 X $184 (2d class) and give you 3 fully covered days of travel (use 2 to get from the Swiss border to your base in the BO, and from there to your departure point). Use the 3rd on whatever is your longest excursion day---ride boats all day, or whatever. Everything else is 1/2 off (and still free for the kids). Plus you get free admission to museums.
