No, do not rent a car, just use the train for the two trips. Just buy normal tickets, NOT a pass in this case. But:
1) How are you getting to Biel?
2) Do not stay in Interlaken. Stay somewhere further into the Jungfrau area (Mürren, Wengen, Lauterbrunnen or Grindelwald). All these reachable by train via Interlaken.
For what to do in this area, and booking hotels, see here: https://jungfrauregion.swiss/en/summer/
3) Why are you staying in Zürich, big city, not mountains? I guess you are actually flying out from Zürich airport. Unless you have an early flight, stay in extra night in the Jungfrau area and take a train direct to Zürich airport. If it is an early flight, stay the last night in Luzern (70 minutes from the airport by train).
Look up train times and prices on the SBB website: https://www.sbb.ch/en
Biel to Lauterbrunnen: 2 hours 3 mins, CHF 46.60
Lauterbrunnen to Zürich airport: 2 hours 45 mins, CHF 81.60
Children half price. On top of that you will probably want to pay for some cable cars when you are there.
From Biel, the one of you not working + child can do lots of day trips by train, Bern, Neuchâtel etc.
