Thoughts on my Copenhagen/Stockholm itinerary?

We leave June 9, Sunday and arrive in Copenhagen at 11am Monday, June
10. Would you take the train from the airport and head up to Stockholm the day we arrive, or would you spend the night in Copenhagen and head
up the next morning?

Personally I would probably spend a night in Copenhagen. But taking the train from the airport to Norrköping is also an option. Although that means you have to figure out how much margin you want in case the flight is late.

My friend lives in Norrköping, which sounds like it is on the
trainline. I am not sure if we are staying with my friend (it is her
children’s last week of school and she won’t be on leave for summer
vacation until July). So we will probably get a hotel in Stockholm and
travel by train to see my friend when it works for her schedule.

Correct, the Copenhagen-Stockholm trains stop in Norrköping. But if you are going to see your friend in Norrköping, staying in Stockholm is a bad idea. You can do day trips to Norrköping but it's 1:15 by high speed train or 1:45 by regional train, so it takes a while. And Norrköping is too often overlooked, it is a charming city with lots of things to see. And plenty of opportunities for day trips. So my recommendation is that you stay at least a couple of days in Norrköping.

One of the things we’d like to see is Lego House, in Billund. I don’t
think we would spend more than a day there. When we leave Stockholm,
would you take the train to go there, or go back to Copenhagen? I am
not sure if there is a train that leaves from Stockholm to Billund…

There isn't, there are no trains from anywhere to Billund. There is no railway station there. You can take the train via Copenhagen to Vejle and then a bus to Billund. Or you can fly, SAS has daily direct flights from Stockholm to Billund.

But, that Sunday, it sounds like my daughter’s cohort/class meet
students at the airport, and the school takes them to where they will
live for the next three weeks. I was thinking my daughter could just
return to the airport with me and meet her group there when I catch my
plane to come back home...

Or she can just ask them and go there herself, that sounds a lot easier than going back to the airport.

We leave June 9, Sunday and arrive in Copenhagen at 11am Monday, June 10. Would you take the train from the airport and head up to Stockholm the day we arrive, or would you spend the night in Copenhagen and head up the next morning?

If your connection in BRU is not too tight I’d plan to continue onward that afternoon to maximize your time.

The challenge is time: you have only 5 full days (Tuesday-Saturday) and 4 cities to visit. If you spend two days in Copenhagen prior to departure and 2 in Stockholm along the way there’s not much time for Billund or Norrköping.

This itinerary is aggressive but gets you around to all 4 cities, albeit with limited time:
Monday: arrive, train-bus to Billund
Tuesday: Billund, fly to Stockholm (4:10pm)
Wednesday: Stockholm
Thursday: Stockholm, early afternoon train to Norrköping, stay a few hours, then last train of the night to Copenhagen
Friday: Copenhagen
Saturday: Copenhagen
Sunday: depart

Yes, this is going to be a rushed trip it sounds like. The above itinerary is not a bad idea, but I'd still recommend a night in Norrköping.

Thank you for the advice and replies! I discussed with my daughter this weekend, and shared the above posted itinerary. We agree it is aggressive, and that the Lego house is something we are willing to give up for this trip - it's her father that is the Lego fan, and he won't be on this trip, so we are going to save it for another time!

Thank you for helping me put it into perspective! =)

That sounds like a wise decision. Removing Billund from the equation will make it a bit less rushed.

Consider visiting the Vasa Museum in Stockholm.

Copenhagen, take a canal cruise and consider a day trip outside of the city to visit the Viking Museum and some castles.

absolutely going to see Vasa!!!

I just booked our hotel in Copenhagen yesterday - The Square. Seems to be a good location, right across the street from a metro stop.

So my plan is: arrive Copenhagen 11am on June 10. Go thru customs, etc. Hotel check in isn't until 3, so hoping they can store our bags, or else we will just find someplace to eat and have our bags with us.

Do you think we would have enough time to do a canal trip that first afternoon?

We have a full day in Copenhagen on the 11th and will head to Stockholm on the 12th, but I just need to find a place to secure our bags if check out is at 12. Maybe it is best if we just head to the train/Stockholm from the hotel...?

These are the things I would like to see in Copenhagen:
Rosenburg Slot, Amalienborg (changing of the guard), Church of Our Saviour, Little Mermaid (I know it is underwhelming), Nyhavn/Canal trip... trying to plot that all out now...

is Torvehallerne markt worth it?

Thinking when we come back into Copenhagen on June 15, we will check out Tivoli and then that's my last night there...

Would love any thoughts and suggestions...
Thanks!
Bridget =)