How many days do you need for Norway?

10 days is definitely not too much! And I wouldn't spend more than 2 nights in Copenhagen, especially since you will spend night 3 in the ferry and thus have a full day in Copenhagen.

We went to Norway in 2018. Family of 4. Spent 10 days and $11,000 dollars, airfare not included. You don’t say how many in your family, but Norway is very expensive, so based on that, 10 days was enough for us.
Here is my trip report.
https://community.ricksteves.com/travel-forum/trip-reports/10-nights-norway-for-family-of-4

Norway is a big country (over 1000 miles south to north) and with multiple climate zones east to west. A 10 day trip would be a sampler tour skipping much of the more rural (and scenic) Norway.

One sampler tour itineary could be:

Multi-city flight itineary to OSL with CPH stopover then return from BGO.

2 fulldays/3 nights Copenhagen

Morning flight to OSL

3 or 4 nights Oslo

Morning train from Oslo S to start Norway in a Nutshell tour (train, boat, bus) via Myrdal and Flam to Bergen. 2 or 3 day with stopover midway through journey.

Arrive Bergen mid-day
2 or 3 nights Bergen

Depart by air from Bergen (BGO)

The above is just a sampel of Southern Norway. There is much more to Norway. See Norway's tourist info wesite: https://www.visitnorway.com/places-to-go/top-10-places-in-norway/

And if you are into slow travel (hiking, skiing)....

Looks like multi-city flight option from ATL to CPH is not very economical if SAS is not a viable option. Best may be to drop CPH and strech Noway.

Norway is a large country and very mountainous. Travel takes a lot of time.

I suggest you consider taking a cruise up the coast of Norway. NCL and Royal Caribbean both have great 11-12 day cruises that go up to the North Cape and stop in several ports.

You get to enjoy the amazing scenic fjords on the ship and then when you get off the ship at the ports, you can take the nutshell tour and others that visit mountains areas.

Norway is very expensive, probably the most expensive country in Europe. In 2019, I remember getting a beer for lunch and it cost the equivalent of $10. It was not a large beer.

By cruising, your lodging and meals are included.

You can do a land tour in conjunction with a cruise, perhaps a shorter cruise that doesn't go to the North Cape. Many cruise lines have them.

Also, in mid-June, the higher elevations have just come out of the snow season where roads are blocked. We visited one port were we were told in mid-June that a week before there was a big snow storm and the roads we used on our ship's excursion were closed.

...appeal of the overnight ferry. Why do people take it?

Tax free alcohol. Alcohol is highly taxed in Norway.

@Tom_MN I stand by my assessment of Norway being expensive. Many others also agree. Can you do it for less than what we spent? Sure. You could sleep in a tent, stay with friends, cook all your own meals, whatever. But, we are not budget travelers and we were not extravagant. Stayed in nice hotels which included breakfast and ate out for other meals. Did the NIN.

I second Edgar’s plan except I would recommend the ferry. Taking the ferry was a fun new experience for us and we were with friends so we socialized that evening. We also bought some duty free alcohol to bring with us as it is so expensive in Norway. But if your time is limited in Norway then flying to Oslo would make more sense.

Norway can be expensive. San Francisco and New York City can also be expensive.

But if you recreate where Norwegians holiday prices can be less expensive. I looked up our group rate half board (breakfast and dinner) cost at the Radisson Blu Mountain Resort, Beitostølen in Winter 2018. We paid $3000 USD for two in one room to our ski association. That's $300 per day for two of us.

During summer months trekking can be less exepnsive. An example DNT 8 day/7 night tour across the Hardangervidda is priced at 11,000 NOK including the 1,500 non-member surcharge. That's $175 per night per person at 9 NOK/USD.
https://english.dnt.no/aktiviteter/139368/903987/

MASSIV IV HARDANGERVIDDA

8 dyas/7 nights We stay at well-built and charming serviced cabins
along the route and one night at a self-service cabin.

Price: NOK 9.500,- from Finse/to Haukeliseter Non-member surcharge
NOK 1,500,-. .

The package includes: Accommodation, tour leadership, all meals
(breakfast, packed lunch/thermos, normally three-course dinner)
except: First day only dinner and last day only breakfast plus packed
lunch/thermos.

No, 10 days is not enough time in any country…….