I totally agree with Tim: do not stay in Interlaken, unless it is a last resort. Interlaken is in sight of the alps, but not IN them, and that is a HUGE difference. Try to stay in Lauterbrunnen, Murren, or Grindelwald.
What you want to do ASAP is to get an apt before they are all rented out. Try VRBO.com or AirBnB.com or Booking.com or interhome.com or tripadvisor.com or Google maps. Other options: see if you can rent out a room for 4 at Valley Hostel in Lauterbrunnen (valleyhostel.ch). They have a common kitchen. Or, if you are campers, you can camp (bring or buy small tents) or rent a trailer at campingjungfrau.ch
As for what to do, there are hiking trails with cows and goats all around and your kids should love that. I'll send a link to your private mail on here to our dozen favorite trails in the area, with maps and pics. (Click on your name in the upper right of this page to read your mail.)
The transportation in the area is superb. No need for a car. If you think you'll make use of a lot of trains and cable cars in the area, you might check out the Berner Oberland Pass (Google it).
You don't say how long you'll be in Switz. but if it's for a short time, I'd skip Bern. The alps are much better, espec. for kids. You could easily spend 2 weeks in the alps (and I have). I know Rick Steves loves Gimmelwald, but Lauterbrunnen or Murren are much better for kids, plus Gimmelwald has no store to buy food. Be aware that Gimmelwald and Grindelwald are totally different places.
Each of my kids were there when they were 13, and now have returned to do it all over again as adults.