"I would think that spending our entire vacation higher up in the Alp mountains to be too long since we are not hiking?"
My main activity in the Berner Oberland is not "hiking." It's looking. If you stay in any of the B.O. towns (Lauterbrunnen, Muerren, Gimmelwald, or Wengen), you are IN the mountains, meaning surrounded by them. All you have to do to see them is glance around, up, or down. If you want to change altitude (going up or down), you again don't have to "hike" if you don't want to (or, in your case, can't due to foot problems). You take a lift or cogwheel train up or down, then walk on flat or nearly flat surfaces.
For instance, you can start in Lauterbrunnen, take the cable car up to Grutschalp, take the train to Muerren, walk through Muerren (almost flat, and fully paved - no mud), take the cable car down to Gimmelwald, walk around a bit of Gimmelwald (some of it is up a hill), then take the cable car down to Stechelberg, then walk or take a bus back to Lauterbrunnen (you can walk as far as you like, then take the bus the rest of the way). All of these run at least twice an hour. Note that the walk from Muerren to Gimmelwald is quite downhill; depending on how you do on downhills, you may want to take the cable car instead. At any point on this circuit, all you have to do to have a great time is look around - the natural beauty is all around.
I agree with the play area on top of Allmendhubel, and that area is great for adults too, with great views of the three peaks (Eiger, Moench, and Jungfrau) without the high price of the Schilthorn.
Yes, Interlaken is flat too. And from Interlaken you can certainly take boats on both lakes, or take train and then bus to the Ballenberg Open Air Museum (a top recommendation for kids - you can go into any room in any building that is not specifically barred, although the most fun ones are often up stairs). In the town of Interlaken itself - well, there are lots of restaurants with varied cuisines (especially Asian ones), and a large Coop and large Migros (department stores with supermarkets, which came in handy when I needed to replace a backpack quickly and cheaply). There are also lots of jewelry stores and sex shops, which probably aren't why you are coming to Switzerland.