All Denmark or add a little Norway?

Your trip is fairly short and you've identified a lot of good destinations in Denmark. Personally, I wouldn't try to shoehorn Norway into this trip. There's a lot to see in Norway: Oslo, the fjord area (the Nutshell route is just part of it), Bergen, the west coast and more. There are some good outdoor activities in Norway your teenagers would probably enjoy. The Voss area, near the Nutshell route, has a variety of options, I think, and there's good hiking just outside Oslo as well as a wheeled bobsled run in Lillihammer. The Norwegians are very outdoorsy folks.

It takes time to travel around Norway, a country with very challenging geography; you keep bumping into water that has to be crossed, often with nary a bridge in sight, so you wait for a ferry. Most towns have a rail or bus link, but the bus links to small places may be only once or twice a day, so renting a car for part of the trip can be very desirable. Because of those factors, Norway's really not a place to go for just a few days.

In case you are not aware, Norway is also eye-wateringly expensive. On top of that, the tourist infrastructure in rural areas hasn't kept up with the demand, so you'd probably struggle to find lodging for July at this point. Instead, I'd recommend doing some research on Norway; it would be worth reading old threads in this forum going back to a couple of years before the pandemic. If it sounds like a great family trip (which I think it would be), you can dig into the details when you get back from Denmark. The first thing to do, I think, would be to nail down lodging along the Nutshell route if you want to spend one or more nights in that area. It will be a lot harder if you wait until 2024 to look for rooms or apartments.

I agree with acraven about leaving Norway for another trip.

That said, when we did a lengthy Scandinavian trip last year we flew from Copenhagen to Bergen with SAS. The flight was inexpensive and we were surprised about how many direct flights were available. So you could fit in Norway in a nutshell using Bergen as your base in 3 days.

Although Oslo is nice (we spent 8 nights there), we preferred Copenhagen and have now been there twice for a week each time.

In Aarhus look into going to Den Gamle By which is the best outdoor museum we have ever been to. It covers from the 1500s to the 1970s. We had a hilarious time on a horse and carriage ride when we realised that cobblestones and carriage wheels don't mix and laughed uncontrollably most of the way.

It covers from the 1500s to the 1970s.

Actually they recently opened a new area about 2014: https://www.dengamleby.dk/en/english/

Also be sure to visit https://aarhusstreetfood.com/en/

And maybe even https://www.aros.dk/en/ (Art museum)

And https://friheden.dk/ (Amusement park)

Adding Oslo and Norway in a Nutshell would in my opinion require at least 4 more days, preferably a few more. So it sounds like a good idea to save Norway and Sweden for later. Or add a bit of southern Sweden. But you can skip Malmö in my opinion, Lund is a better option for a day trip from Copenhagen.

Thank you very much for your comments, everybody. After reading them and doing more research, I decided to stay the whole time in Denmark, with maybe a stop in Ystad or Lund (thanks for that comment about Malmo vs Lund) I'm still not sure if spending 3 nights in Odense and 2 in Arhus is better than just extending our stay in Copenhagen and using it as a base to take day trips. If anyone has any thoughts, I'd love to hear them.

I've been doing more reading from the forum and contributors' comments have been very helpful.

There's a tremendous amount of good information in older threads here. I used that source heavily while planning my 2022 trip. There's not so much posted about Scandinavia that it becomes overwhelming (as is the case with Italy, for one example).

You could add a bit of Sweden as it is close by. Not spending all your time in Copenhagen is a good idea. In the end it depends on what you are looking for and what brings you to Denmark.

Consider a daytrip from København to the ancient city of Roskilde, which was a hub of Viking land and sea routes more than a thousand years ago. The capital of Denmark until 1443, Roskilde ( Danish for “Cathedral”) was where a number of Viking ships were discovered and now can be seen at the Viking Ship Museum. Roskilde’s Cathedral, completed in 1275, is where 39 Kings and Queens of Denmark are buried. The city is only a 25-minute train ride from København’s Central Station,

Do Norway later.
When you I, I suggest taking a cruise up to the North Cape. Royal Caribbean and NCL both have great cruises, usually in the Summer.

You get to see the great fjords from the ship, then take excursions from the ports to great scenic places.
Also, you save on lodging, meals and transportation in Norway. Norway is one of the most expensive countries in Europe.

Last August my family (myself, husband and 2 teens) did Denmark and Norway in one trip. About 12 days. It was a whirlwind. Sure it was doable but we were going non-stop and packed so much in. We had a great time, loved it all but if you feel your family are the type that might tire from the constant on the go then maybe save Norway for another trip.

If you do decide to add Norway we did the overnight boat to go from Denmark to Norway. It was a fun experience and a smart way to use our sleeping time travelling to our next destination.

As for traveling with teens mine loved Tivoli Gardens in Copenhagen don't miss that. They really enjoyed Copenhagen overall and the fjords in Norway. Have fun!