I think I just found the answer for anyone else who may stumble across this thread. It appears the Family Pass does require the Swiss Pass/Card, not a normal ticket. However there is a 1yr Junior Travel Card that you can buy for CHF 30 that covers allows them to travel on all trains for free with a paid adult, including normal tickets and mountain trains I believe.

http://www.myswissalps.com/juniortravelcard

I plan on picking up two of those in Spiez, then just pay cash for the adult tickets while in Switzerland (with 25% Eurail discount) instead of getting the Swiss Pass/Card. Do I need to "buy" (for free) tickets for the kids using the Junior card so they'll have a proper head count on the trains or just show the card itself?