Hello Vlasta, and welcome to the forum! If you want travelling to be easy, a Swiss (Saver) Pass
would be a good choice. It allows you to get on and off trains, buses and boats without having to purchase tickets for each trip. Mountain transportation is discounted though, so if you want to make use of cable cars and mountain trains, you do have to buy disounted tickets (this goes for almost all Swiss rail passes). Especially for your second week, in which you want to explore as much of the country as possible and probably will be making many long train journeys, a Swiss Saver Pass will be worth its money. I'm not quite sure if this is the case for your first week in Lauterbrunnen as well. If you'll stay within this region and explore the Jungfrau area only (Lauterbrunnen - Mürren - Grindelwald - Interlaken), you might be better off with a Swiss Half Fare Card
(which does require you to buy discounted tickets) or with a Jungfraubahnen Railways Pass
. So you could take one of these for your first week and an 8 day Swiss Saver Pass for your second week.
To make sure which pass (or combination of passes) is most economical, you should calculate the costs of the exact journeys you have in mind and compare the discounts of several rail passes. Please follow the instructions on this in our rail FAQ
A Swiss Saver Pass is indeed one ticket for all people using it, so if you order one Swiss Saver Pass for the entire family, you should travel together to profit from its discounts. Of course your travel party can split up as well, but in that case only one of you can take along the Swiss Saver Pass. The other ones will have to travel without it. You could also choose though to purchase several Swiss Saver Passes. A Swiss Saver Pass is available for 2 people or more traveling together. This means that you could purchase one Swiss Saver Pass for two or three people out of your travel party and another Swiss Saver Pass for the remaining ones, based on which ones of you will probably be travelling together most of the time. There's no difference in costs between one Swiss Saver Pass for the entire travel party or two Swiss Saver Passes for couples/smaller parties. This makes splitting up and still using your Swiss Saver Pass easier.
If this is not a good solution for you, you should consider the regular Swiss Pass, which is individual (but more expensive) or another individual pass. Saver variants only exist for the Swiss Pass and the Swiss Flexi Pass. All other types
mentioned are individual passes.
The Swiss Saver Pass (and other Swiss rail passes) can be purchased either online
(please review the header 'Order your Swiss Pass here') or locally at larger Swiss railway stations. It depends on exchange rates and shipping costs to your country of residence which option is cheaper.
You could take a look into the overview of hikes
and day trips
in the Bernese Oberland to find out which activities appeal to your children.