itinerary suggestions 1st time visit: 3 days

First see what the flight options from BCN are, then pick one place. Lucerne is very convenient to Zurich and in addition to being a lovely town, is well positioned for day trips to mountains.

You don't say when you're visiting, so hard to suggest for sure. With 3 days I'd probably just stay in Luzern and do something like this:
Day 1 - Fly into Zurich, store luggage at the train station and explore Zurich for a bit, then train to Luzern for 3 nights
Day 2 - Explore Luzern (boat ride, go up the mountain to Rigi, etc.)
Day 3 - optional day trip to Bern or more exploration of the Lake Luzern area (possibly Stoos Ridge hike?)

OR, if you want to experience being more up in the mountains, then do something like this...
Day 1 - Fly into Zurich and train to Grindelwald (store luggage in Bern on the way to see the city), stay in Grindelwald or Wengen for 3 nights
Day 2 - Mannlichen to Kleine Scheidegg with optional up to Jungfraujoch
Day 3 - Murren, Schilthorn, Lauterbrunnen

sorry, we're going in mid July. I've not done research yet on my kiddo's latest request: Kandersteg , Grindelwald, and Lavertezzo for hikes. A quick google search makes me think that lavertezzo is too far.

With three days (hopefully you mean 4 nights giving you three full days) you only have time for one location, IMO. Go to Grindlewald and day trip to Kandersteg or Bern or Luzern, if you must. You may find yourself so enchanted with the great Jungfrau area you won't want to go elsewhere. Time is of the essence regarding lodging. July is super busy. If there is nothing that suits you in Grindelwald, try Lauterbrunnen, Wengen, or Mürren for a great mountain location.

Luzern itself is also a good choice for3 or 4 nights with LOTS of daytrips possible. You just cannot go to nor see every place on his ever-growing list.

Yes, Lavertezzo is too far out. And by Kandersteg I'm assuming he means Oeschinensee. I think the issue is that often when you look online or on social media at highlight reels everywhere looks tempting because it's all amazing, but if you try to do it all you just spend your time running around seeing trains and hotel check in desks. A base in Grindelwald can give you amazing hikes, lakes, etc. that will fulfill the highlight reel without having to move around and hit these places that appear often on "best of" reels, etc. You could also stay up in Wengen to experience a car free village, which is very unique to Switzerland.

In July you can do some amazing hikes that give you lake views to replace the Kandersteg (Oeschinensee) request, such as going up to Schynigge Platte via the cog train and hiking to Oberberghorn on the ridge. The red trail on this blog post - https://fullsuitcase.com/schynige-platte-hikes/

You can also go up to the Schilthorn and even hike down to Grauseeli to swim in an alpine lake that you'll probably have to yourself. https://schilthorn.ch/24/en/Birg-Grauseeli
https://www.alltrails.com/trail/switzerland/bern/schilthorn-grauseewli-birg

You can hike from Mannlichen to Kleine Scheidegg on the Panorama Trail and then go up to Jungfraujoch or over to Grindelwald First with additional options to Bachalpsee.

There are endless suggestions in this area that would fulfill the wow factor, but that's just a few. I'd highly recommend for 3 days picking just Luzern or just Grindelwald/Wengen. And since you're going to Barcelona, Paris, etc. skip the cities and immerse yourself in the Alps that make this area unique. You'll get your fill of European cities on the rest of your trip and places like Zurich and Bern are secondary to the mountain experiences when you're already going to other European cities.

With Kandersteg and Lavertezzo on the wishlist, it sounds like the kids have been looking at Instagram hits.

Unfortunately Oeschinensee is an Instagram victim; apparently it lbecame so popular in the post-pandemic rush that our favorite hotel by the lake, Berghaus Oeschinensee, closed after the 2022 season due to what the owner described as a “toxic environment” created by too many “entitled” people showing up. They could not keep staff hired. But the restaurant remains open, and the smaller hotel by the lake is still open.

If Kandersteg is still a “must” I suggest you do it the Swiss way and spend a night, either in the mountain hotel by the lake or one of the SAC huts above (not Blümlisalphütte, that hike is long and tough). Fründenhütte is in a spectacular location reached by hiking natural ledges in the cliff face, with cables for security. We have not been to Doldenhornhütte so I can’t compare. You can see all these options, and check for reservations, on this website:

https://www.oeschinensee.ch/en/uebernachten/

But I wouldn’t dismiss Lavertezzo as “too far”, and in many ways it makes a better destination than Kandersteg, to my mind at least. The train over the scenic Gotthard Pass to Locarno from Luzern takes 3 hours, only 30 minutes longer than the train from Luzern or Mürren to Kandersteg. Stay 2 nights in Locarno and use the intervening day to visit the Val Verzasca by Postbus. I believe Lavertezzo is 45 minutes away; buses run on schedule. Then fly out of nearby Milan to your next destination.

https://www.ascona-locarno.com/en/explore/valle-verzasca

So either of these could be added to a visit to either Luzern or the Berner Oberland (hopefully you do have 4 nights).

If it is only 3 nights, best limit your Swiss time to one location—-either Luzern or Berner Oberland. There are lots of adventure activities (zip line, Trotti-bikes) as well as good hiking on offer at Grindelwald, so don’t feel that staying in one of the smaller mountain villages is mandatory.