Interlaken with baby

Take the train south to Lauterbrunnen or Grindelwald. Both are less than 30 minutes away. While there you can do easy strolls and enjoy the incredible scenery. The scenery will be much, much better than in Interlaken.

Don't stay in Interlaken. Just get a nice hotel in Lauterbrunnen (in the valley surrounded by alpine peaks) or in those high alpine villages of Wengen or Murren with those drop-dead gorgeous views. All of these places have nice hotels, nice restaurants, sports centers with swimming pools, etc. SOOOOOO much better than Interlaken.

We will be driving. I have been to some parts of switzerland and I am aware that there are some places wherein cars are not allowed. If we will be staying in lauterbrunnen or wengen, can we go there by car?

You can drive to Lauterbrunnen. Muerren and Wengen are car-free, so you would park below and take trains or lifts up.

I'd also recommend staying in Lauterbrunnen, as it's accessible by car and there's parking. That's a good place to use as a "home base" for touring that area, as Lauterbrunnen is the transportation hub so you can easily get to either side of the valley for day trips. You might enjoy visiting Mürren via cable car and mountain railway (referred to as the "BLM" route), take a trip to the revolving restaurant at the Schilthorn and return via Gimmelwald and the Post Bus from Stechelberg. It sounds complicated but it's all very easy.

Which places you visit will depend on your budget, as the mountain lifts can be expensive. Depending on how long you'll be there and which places you might like to visit, one of the Swiss passes may be beneficial.

If you were planning to visit the Jungfraujoch, one caveat to mention. The facility is at about 12,500 feet / 3800 M and it might not be advisable for a 1 year old baby. You might want to discuss that with your family Physician. The Schilthorn is at about 10,000 feet / 3000 M so it's not quite as much of a problem.

We did it with our 10 month baby with doctor's consent. It went well. We had more problems with our 11 year old. Murren is best several easy GREAT hikes.