Hi heather.nicole.hansen, and welcome to the Forums.
I just stayed a week at a hotel on the other side of the Zurich airport from the terminal.
I drive my own car from home (England) and have been to Switzerland many times.
I'd like to caution you about a couple of things regarding the car hire at Zurich airport and a couple of the legs you have planned, based on my very recent experience.
By far the shortest, most scenic and usually fastest route from the airport to Lauterbrunnen is the autobahn via Luzern. Going around via Bern adds at least 90 minutes and isn't really special until you reach Thun and then again after Spiez.
The problem is that there is a lot of road construction going on on the road from Zurich to the road to Luzern. Swiss construction zones are a restricted speed which is camera controlled. It is also not especially easy to see where to go with the orange lines on the road. The problem gets worse on the road between Interlaken and Brünig/Meiringen, the A8. Virtually the entire length of Lake Brienz, the motorway is one lane segments where the cars (and trucks and buses) go both ways on the same lane in turn, controlled by traffic lights. These are very long waits, and in the sun. My trip which should have taken about an hour between Interlaken and Luzern took well over 3 hours.
It is a shame because I love that road, and have recommended it many times here, especially the sequences of very steep corkscrews coming down the pass from Brünig towards Meiringen. Although, to be honest, I prefer the train on that route. Panoramic windows in all carriages (so I, the driver normally can see the scenery too) - and in the car you get much less views of the lakes and waterfalls. No wonder it is a narrow gauge cogwheel train. It has to be.
One other thing about that road - it is one lane each way and for almost the entire length there is no passing allowed (or advisable). Solid line down the middle of the road. (strange ideas about motorways - autobahns - these Swiss have!!) so if you get behind a bus or a truck or a tractor you are stuck until they pull off.
Be sure your car has a parking clock and carry plenty of large coins for parking. In most cases you will park in a space, note down the space number and your car's number plate - you could need either, and in Zug and Zurich, both in many cases - and find the Zentrale Parkuhr machine (have a look at this wiki article) https://de.wikipedia.org/wiki/Zentrale_Parkuhr
I hope the drive from the airport is after a short flight, not an intercontinental one, because you'll need all your wits about you - something many people have trouble with after a long flight.
One great thing using a car gets you is the chance to eat at Mövenpick Marché, which are at several motorway rest areas, including one east and one west of Zurich, and one north of Luzern, and one in Heidiland among others. We love them.
One thing you and your boy may like about train travel is that almost all trains have toilets in many of the coaches so no having to pull over and find somewhere on short notice, and he is free to get out of his seat on the train, which is most def not allowed in the car.
Just FYI, Swiss fuel, petrol and diesel, is in a race with the British for most expensive in Europe. Last Sunday I had to put in fuel because I didn't have enough to reach Germany. I paid CHF 2.425 per litre, the cheapest I could find around Luzern. That's 3.79 litres per US gallon so CHF 9.19 per US gallon. That's about $9.56 US a gallon.
Forewarned is forearmed.
I think the three of you will love Switzerland. There's a reason I'm back every year.
To be continued - ran out of space....