As someone who has traveled to Switzerland numerous times with teens, and one time doing a Swiss heritage trips based on my husband’s Swiss relations, I have some comments.
I would not stay in Gimmelwald. I know Rick promotes the place, but there is no town there, very limited lodging options, and zero restaurants. You and your kids would be much happier, in my opinion, staying a , a combined boat plus train journey that bit higher up the hill in the car-fre village of Mürren. With 5 people, you might need an apartment as most hotel family rooms are limited to 4. On a tight budget I would suggest Chalet Fontana, in the ground floor apartment. We stayed there several times. Or ask here for more recommendations. Chalet Oberdorf, a 3-bedroom apartment with speculation views from the living room and the decks is our favorite.
For your visit to Sonvico, it makes sense to make your way to Lugano , as Sonvico is a short bus ride away.. A nice way to travel between the Berner Oberland and Lugano is to take the scenic Gotthard Panorama Express a combined boat plus train route that uses a route over the Alps instead of under them in a tunnel as most of the fast trains do. You would need to start in Luzern which is well,worth a visit.
From Lugano you could make your way by bus and ferry to Varenna on Lake Como, a lovely small town right on the lake. From there to Cinque Terre is an easy journey by train, with a single train change at Milano Centrale if you choose the right connections.,
Chamonix does not fit easily into this itinerary.