Hi Kay, and welcome to MySwissAlps!
We don't create itineraries for people here, but will assist you to refine one that you have created yourself :-)
For a first visit, given the time you have, you might want to base yourself for half the time in Luzern/Lucerne and the other half in the Jungfrau Region (Lauterbrunnen, Wengen, Mürren or Grindelwald). Interlaken is also an option, but lacks the charm and beauty of the alpine villages.
There is a wealth of information on this site. Perhaps you could start with the following:
How to compose an itinerary for a trip to Switzerland
www.myswissalps.com/pl antrip/doityourself/co mposeitinerary
Car or train
Don't forget to consider what type of vehicle you would need for 5 people and all the luggage you say you will be bringing.
Where to go
What to do
We look forward to seeing your itinerary and assisting you to refine it.
April is between the ski season and the hiking season, so some mountain transport will be closed for maintenance, or will not yet have reopened after the winter break. Dates and duration of maintenance closures vary from place to place. If we know the dates you will be in particular locations, we can tell you what will be operating and what will be closed.
Hiking in April will mostly be limited to low altitudes.