Some partial answers -
The trip seems reasonable....you are giving each place/region a couple of days, and not trying to do an impoosible number of things in a short trip. Once you see how many choices and options there are, you may wish you had a few more weeks. ;-)
There are nice places to hike all around Lake Luzern (German spelling for the name). Many involve climbs and descents ( on very good trails or roads) of a few to several hundred meters.. There are some scenic easy ones, as well. Many can be reached by train, or lake boat, or bus.
For an example, walks on the upper parts of the Rigi are very scenic and can be easy or difficult, as you choose.
Trains up to Rigi Kulm (top) are quite scenic. The one from Vitznau has better views.
Once you are in Luzern main station, go to the tourist info office by track #1. Talk to them about hikes appropriate for your family.
The train route to/from Luzern/Interlaken, via the Brunnig Pass is a reasonably scenic route.It will be covered by various passes -- some half fare, some full fare.
The train rides near Jungfrau are very scenic. covered to varying degrees by the passes. Once you get past "inter-urban" trains and get on "Scenic Excursion Trains" such as from Kleine Scheidegg to Jungfraujoch, discounts diminish. These latter are privately run railroads, not part of the public transport system
Arno says this before your response:
<<"Q1: You'd better consult your pediatrician. In general it's not
recommended to take children under 2 to places above 2500 m. Please see
our Jungfraujoch page.">>
You then say:
<<"We will then move to Interlaken in the evening and visit Jungfrau the day after. After returning from Jungfrau,">>
I think that there is a disconnect.