Family trip Itinerary advice needed PLEASE!

Renting a car in one country and dropping it off in another incurs very large drop-off fees. The train systems of both countries are excellent, and I’d guess the kids would really enjoy the train rides. I’d suggest dropping off the car just after your Parma tours.

https://search.ricksteves.com/?button=&date_range=1y&filter=Travel+Forum&query=Switzerland+itinerary&utf8=%E2%9C%93

Above is a link to recent discussions here on the Forum; it's been a very popular topic. Perhaps there are helpful hints you can use. Also just review posts under the Switzerland section here.
This summer Europe will be very crowded, as many folks have not been across the pond since 2019. I'd encourage you to plot your itinerary and book lodging asap.
Have a great family trip.

Don’t bring the car to Switzerland. Drop it off in Italy to avoid big fees. You won’t need it in Switzerland. Your older kids will get Swiss train passes for 30€, youngest is free, so take advantage of that. https://www.myswissalps.com/swissfamilycard

Everywhere you want to go in Switzerland will be touristy. Lean into it. Expect crowds at peak seasons. Everything you’ve asked for is available in the Berner Oberland area.

You won’t find hotel rooms that sleep 5. You’ll need two rooms, or a rental apartment. Camping Jungfrau is an option in Lauterbrunnen. They have little cottages that sleep 6. https://www.campingjungfrau.swiss/en?utm_source=gmb-camping&utm_medium=organic

You will want to a reserve asap as lodging is limited and this summer will be very busy.

Interlaken being touristy and Murren not is a false dichotomy. Both are about as touristy as the next. Grindelwald is a town that is probably more touristy than both you mention above in the same area. It's not a bad town but buses go there.

Gimmelwald is arguably less touristy, but there's less to do too, and you're as far as you can get down the Lauterbrunnen Valley cul de sac. In the Berner Oberland my family's preferred village is Wengen. Murren has more dramatic views of the huge mountains, but Wengen also has views of these mountains, and an amazing view down the valley. Out of all of the BO villages Wengen is about the most central in the mountain transit network, so you can get everywhere easily and quickly. Plus there is a lot to do in Wengen itself, especially for kids. It has more municipal infrastructure than some of the other places that are more destination ski resorts.

But the differences between BO villages are minor shades of gray. There aren't bad choices!

If you want a less busy, less touristed and far cheaper place to stay than the areas you mentioned in Switzerland, check out Tannheimertal. Several good villages to stay but we like Tannheim. It's fabulous for kids. There's a great playground, an affordable and fun indoor climbing gym in the community center, a big public pool with water slide that is right next to a big swimming lake with huge lawns and a restaurant, a big beautiful Alpine Lake, a network of lifts and traditional huts, bicycle trails all over the valley floor, working agriculture so lots of cows and pigs and sheep and chickens, some absolutely insane Baroque churches, lots of hiking, via ferrata courses of all levels, mountain coasters nearby, good areas for ice cream strolling, seemingly non-stop municipal festivals of one sort or another. In 3 weeks spent in the area my family encountered one other set of English speaking tourists.

A car is handy, and probably why English speaking tourists don't know about this place.

https://www.tannheimertal.com/en/

One more little bit of Tannheimertal spam, since I often feel as if I'm the only American who's ever heard of the place. Apparently the region won by a landslide a poll about which of 18 hiking regions in Austria was best. Quoting from the tourist board

The Tannheimer Tal is Austria's most beautiful hiking region

A small idyllic valley with great qualities. This was also the opinion of the readers of the German Wandermagazin. They clearly chose the Tannheimer Tal as the most beautiful hiking region in Austria. Above all, the versatility of the offer was praised. With a very impressive result the Tannheimer Tal won the title "Austria's most beautiful hiking region 2019". Of the 7577 readers of the German hiking magazine who voted for it, an impressive 71.45 percent voted for the idyllic valley in northern Tyrol. A total of 18 regions applied for this title.

You don't need a rental car in Berner Oberland. I've taken my teens there several times and they loved it, and even returned to the same places as adults. Click on my name here and you can find our favorite hikes.

Thank you all so much! These recommendations and the links for family hikes are all great!
It looks like the consensus is to return the car on the Italian side and use the trains afterwards. I'm thinking a night in Lugano, followed by 4-5 nights in BO area where we can explore various mountain towns, then make our way back to Zurich for a night ( don't want to stress about getting to the airport the next day)!
Does this sound ok or should we push to do a night or two somewhere else? Are there any places that I shouldn't miss this time around?

Also, the Austrian Alps look AMAZING! Definitely adding to my travel wish lit! If not for DH having wanted to see Switzerland his entire life, I would go there this trip!

I recommend you buy two (2) Half Fare Cards for 120 CHF each plus get the free Family Card and the kids ride with you free, the 4 yo is always free, but you need this for the other 2. That will give you 50% discount on tickets from Chiasso to Lugano to Luzern.

Also buy two (2) 6-day Berner Oberland Passes at 220 CHF when you have Half Fare Cards. That will cover you from Luzern to the Berner Oberland location and free rides on many mountain lifts in the B.O. region for your stay. When you leave for Zurich, they will cover you to Bern or Luzern depending on your route, and then the Half Fare Cards ive you a 50% discount the rest of the way.
https://www.berneseoberlandpass.ch/prices-tickets/
https://www.sbb.ch/en/leisure-holidays/inspiration/international-guests/swiss-halffare-card.html

Yeah your plan sounds fantastic. Have a wonderful time :-)

I've been planning our trip to the Alps for 2 years. Look into the availabilty of summercards, which give you a discount/free access to cable cars, trains, busses and other activities. The Appenzeler card looks like a pretty good deal, and though I didn't read the details, some of their hotels offer "arrive free" deals that include passes that cover the cost of train travel to Appenzell.

My interest in Appenzell was fueled by fascination in the geology of the region, and in particular, Santis mountain, which is on a uplift ridge described by a Swiss geology professor as the most interesting formation in the country. I do believe the gondola to the top of Santis is covered by the summercard. We will not be in the area long enough to get one, but have made reservations on Lake Brienz (Interlaken/Lauterbrunnen) at a hotel with a pass that includes free boat rides on the lake and train ride to the top of the Rothorn. We also are taking advantage of a summercard in San Moritz that includes free use of the public transporation, mountain railways, and part of the Bernina express.

Just include "summercard" when you search for lodging. Also, think about the Swiss rail cards which include discounts on attractions, including cable cars.

Lauterbrunnen is spectacular. We have been to the area twice but believe it is one of the most beautiful places on the planet. Recommend Trummelbach Falls and the cable car to Schilthorn, but encourage you to get up early so your views aren't lost to developing clouds at the higher altitudes. Is expensive, which may justify the rail pass, especially if you are arriving by train from Italy. Not far away are Reichenbach Falls and the Aare Gorge, which are amazing, and the falls is where Sherlock Holmes fell to his fictional death, accessible by public transport and not as expensive.

As I keep reminding myself, wherever you are in the Alps is beautiful. Create an itinerary that recognizes you have a little one who has unique interests. And that may make it worth looking at places near Lake Lucerne and Mt. Pilatus, with the Lucerne Pass, that covers chocolate tasting in Lucerne, boat rides on the lake and an amusement park at the top of Mt. Pilatus.

I hope that helps you complete your itinerary. Have a wonderful summer.