You have definitely scheduled a wonderful trip. How you divide your time really depends on how much hiking you want to do. We are returning to Lauterbrunnen for our 4th visit, our most recent was in 2023. This time we are staying in Grindelwald, the last time, we found the lovely little village of Isenfluh after a 2-night stay at Giessbach Hotel, which we recommend highly, and the train trip up to the Rothorn from Brienz. . Using the cable cars quickly gets expensive unless you've bought a Swiss Travel card and trains for your excursion. We have always traveled by car because we headed to remote locations and had gear that would make train travel for extended times difficult. We loved the trip up to the Schilthorn and a visit to Trummelbach Falls on a trip where Lauterbrunnen was our base. We used RIck Steves' guides to get around, but we never made it to Gimmelwald, and because my husband may be using an electric wheelchair this trip, we opted to skip it again. It might well be the prettiest spot in the valley, but just being there, staring at the waterfalls spilling down the cliffs and the great peaks in the distance clears my head and nourishes my soul. It's one of those places that virtually every view is awesome.
This trip, we are staying near First, just outside Grindelwald, and think there are activities there that your children will enjoy if you head up to First. If you are traveling by car, there are some amazing sights to see near Meiringen, including the funicular up to Reichenbach Falls known as the place where Sherlock Holmes died. The Holmes connection is a bit corny but the ride itself is beautiful. Deeper into the Alps, beyond Meiringen is one of the steepest funiculars in the world. I believe it's called the Gelberbahn. That should be one of the most memorable activities of the trip.
We are making our first excursion into Kandertal, the valley to the west of Lauterbrunnen. It is a bit different, a bit wider, and it has many lovely alpine lakes. You might want to add a few nights there. Or head to Stoos, which is on a lovely plateau just east of Lucerne. Again, a great funicular that rolls as it climbs to the top. And good accommodations.
With a group of teens/tweens, I think you decision to make Lauterbrunnen your primary focus makes sense. There are plenty of beautiful places to see, but it means train or car time. You are heading to one of the prettiest places inthe world and there are enough cablecars and kayak companies in the region between Lauterbrunnen and Lucerne that you'll find plenty of lovely places to hike and vistas to enjoy.
Have a fantastic trip.
Despite being to Interlaken multiple times, we've not spent much time in the nearby Swiss cities, though Lucerne looks lovely. On our last trip, we were knocked out by the beauty of Lake Uri, as we drove along it's eastern shore toward Brienz. We are now debating whether we should stay near Lake Uri and enjoy a boat ride or should stick with our original plans to spend a few days at Lake Walensee, which doesn't draw huge international crowds. Some of the longer boat rides if you are staying in or near Lake Lucerne will take you into Lake Uri, and the ride will be unforgettable.
We enjoyed Montreaux and Chillon Castle very much and had a wonderful stay just outside the city, with views of the Alps beyond the lake that were glorious.