Although we are the ticket experts here, I wondered if your itinerary makes sense. Since you said it is your lifelong dream to see the Switzerland, why wouldn’t you want to see the mountains, the Alps, for which Switzerland is famous? The Alps are beautiful in February (see: https://www.restaurant-winteregg.ch/bilder-album/winter/b/winter_04.jpg). In the contrary, there is nothing that could hold you in Zurich or Basel, these are rather boring cities in the winter time. And, by choosing Zurich or Basel as your base, you will not be close to the Alps.
If you want to see scenery and the Alps, travel Basel-Lucerne-Interlaken (or Wengen, or Mürren, or Grindelwald), and back to Basel. Lucerne, as well as Interlaken, offer both direct trains to Basel SBB, from where you can hop on the bus service to the airport. As February is high season in Switzerland, you might find it difficult to find a hotel. I can suggest the youth hostel in Interlaken. It is modern, quiet and conveniently located at Interlaken Ost, which is the train hub for all trains to Lucerne, Basel, and Lauterbrunnen / Grindelwald.
In Lucerne, consider going to Mt. Rigi instead of Mt. Pilatus. The views are much better from Mt. Rigi and you could combine it with a lake cruise.
A 4-days Swiss Travel Pass might be worth, it covers all your travel, and it comes with a complimentary Swiss Family Card (ask for it); with it, your son travels for free when accompanied by you.