Two Weeks! How much is too much?

Since you've got a year, I suggest you look at Rick's suggested itineraries not only for selected countries, but for 2 weeks in Europe. Not that you need to copy what he suggests, but you can lift portions of them and mix and match into a trip.

You could also check out Conde Nast Traveler's recommended travel agents and interview a few, they are paid to know stuff.

Be aware that Hallstat is overrun with tourists these days, https://www.bbc.com/news/av/world-europe-49171477/hallstatt-a-town-of-800-people-that-gets-a-million-tourists-a-year.

If you go to Lucerne go to the city wall of the Old Town. There are wonderful views from the Musegg wall and towers. We entered from the ramparts from the Schirmer Tower. There are lots of wooden steps to climb. You can walk along the upper wall from the Schirmer Tower to the Clock Tower and Wachturm and back. The Clock Tower has a great clock museum inside. The Nine Towers provide great views of the town of Lucerne and Lake Lucerne. The city was very crowded at the end of June and this provided a shady respite for us.
For a train ride the Golden Pass Panoramic Train via the Brunig Pass from Interlaken Ost to Lucerne had gorgeous views.
My husband loved the Glacier 3000 trip that he took on an excursion from Lausanne and walking on a suspension bridge between 2 mountains, lunch there and amazing views.
The Chillon castle near Montreux was also interesting. The Lavaux Vineyards are spectacular near Lutry and Vevey overlooking Lake Geneva.
If you go to Switzerland you could fly into Geneva and out of Zurich or vice versa to avoid backtracking.
I hope you have fun planning this trip!

A very not-touristy place to go would be the Canton of Valais. We spent a month here several summers ago and loved it. I think we were the only Americans as we heard no American English the entire time we were there. There are many castles in various states of ruin and repair - for some of them you will be the only one there. The town of Sion is a nice little, not very touristy place to go and has a castle perched at the top of a mountain in the middle of town...really great example of a castle from this region. Ask the caretaker to show you the frescoes that he keeps under lock and key! There is also an ancient church perched on the top of the neighboring mountain in town - almost completely unaltered since it was built in the 12th century. The old part of the city is still partially walled. There are many other castles dotted up and down the valley - many of them are unattended - you can enter and you will be the only one there. That area is surrounded by year-round skiing in the 4 Vallees ski area of Verbier, Nendaz, Mont Fort, La Tzoumaz, and Veysonnaz. Amazing mountains and a view of the Swiss, French, and Italian alps from the tops. Easy access also to Kandersteg and the Berner Oberland by a car train through a tunnel from Lotschberg - so much fun! There is a stunning lake surrounded by high alps in Kandersteg just at the other end of the tunnel. You can take the gondola up from town, walk along a paved path for about 15-20 minutes and you are at the beautiful Oschinnensee. The only ice cave in the region of Valais that I know if is at the far north end of Valais at the Rhone Glacier. It's a little depressing though because the glacier is melting fast and they have tried to prevent their ice cave from disappearing by draping it in canvas. It's a rather sad looking sight.
The only two things on your list that this area does not tick off would be a salt mine and Lucerne...other than that I think it might be what you are looking for.

I have a couple of suggestions that combine your desire to see Gimmelwald again with Anita’s suggestion of the Valais region.

Start with a stay in Mürren ( just up the hill from Gimmelwald) for 4-5 nights. We spent a week there last summer in this 3-bedroom, 2 bath apartment, which would be great for our family.

https://www.tripadvisor.com/VacationRentalReview-g188084-d6588573-Chalet_Oberdorf_Murren-Murren_Jungfrau_Region_Bernese_Oberland_Canton_of_Bern.html

It has two large decks and great views across the valley to the Jungfrau massif. While in Mürren, your husband can do the famed Via Ferrara. Take your child up the Allmendhubel funicular and a nice playground. Thenreturn to Mürren on the childrens’ Adventure trail, which incorporates a series of slides, tunnels, and log crossings to accomplish the descent. My grandchildren ( age 6) did that and loved it.

Your husband can depart on Day 3 to the Jungfrau on the other side of the valley. There he can meet his guide for the 2-day trek down and across the glacier to the Marjelensee and the tiny village of Fiescheralp.

https://old.myswitzerland.com/en-us/zo/glacier-hiking-tour.html

https://blog.outdoor-interlaken.ch/2018/08/13/aletsch-glacier-hike/

You depart Mürren on day 5 and travel to the hamlet of Bettmeralp, a car-free village like Mürren. This is a short hike from Fiescheralp and your husband can meet you there. Spend 3 nights in Bettmeralp——there is a great zip line/ropes course designed for small children that my grandsons absolutely loved. They are provided with helmets, gloves, and harnesses. There is also a swimming lake above town, several lifts to ride, and wonderful views of the Aletschgletscher.

https://www.aletscharena.ch/sports-summer/climbing/rope-garden-baschweri/

https://www.tripadvisor.com/Attraction_Review-g1096327-d8445686-Reviews-Seilpark_Baschweri-Bettmeralp_Canton_of_Valais_Swiss_Alps.html

https://www.aletscharena.ch/destination-en/photo-gallery/

If you time your visit to be in Mürren over the first weekend in August, you will experience the village Dorffest (festival) with a parade of decorated cows, bands, etc.

https://www.tripadvisor.com/LocationPhotoDirectLink-g188084-i127638778-Murren_Jungfrau_Region_Bernese_Oberland_Canton_of_Bern.html

Like the person above, I fear it may be too late to visit Hallstatt. It is now overrun with tourists; maybe worse than Venice. Also maybe too late for ice caves.

There is summer skiing at Zermatt on the high glacier, but the quality may not be worth the price. Look at www.zermatt.ch for more information on Zermatt.

There is actually a salt mine in (or near? it might be in neighbouring Vaud) Valais: https://www.seldesalpes.ch/fr/mines-de-sel/