Itinerary help in Copenhagen with day trips

I was in Copenhagen last summer and went touring with a colleague. She took me to Rosenborg Castle which I very much enjoyed and would think children would as well. There was a special toilet and jewels and a mirrored room! There also are beautiful park grounds.

My friends had a small boat and took me on a canal tour. I saw the tour boats which are interesting. They are really low and wide to fit under the bridges. Your children will love it, as will you.

I walked by Tivoli Gardens many times but as I was not with a child I did not enter.

Beth

Will you have a car? Without one, Mons Klint is not easy to get to.

I'd certainly recommend a day trip to Roskilde, where you can visit the Viking Ship Museum and the cathedral

Tivoli is certainly a top attraction in Copenhagen (even for us older "children"). The kids are likely to enjoy visiting the Round Tower as well.

I agree that the harbour boats and Roskilde are good options for kids.
To plan all your day trips use www.rejseplanen.dk for all public transport.
Møns Klint is spectacular and great for kids, but it is a long trip from Copenhagen. It was covered in another tread not long ago. https://community.ricksteves.com/travel-forum/denmark/copenhagen-to-mons-cliffs
Helsingør and Kronborg Castle should be interesting for kids and Louisiana might not be bad for the kids either, but to be honest I have never actually been to Louisiana.
Going to Malmø just to cross the bridge and get currency seems like a bit of a waste of your time. The train runs underneath the regular road on the bridge and much of the views are obscured, so you only really see water.
Other things kids might like in Copenhagen are the Round Tower and climbing the spiral staircase on the spire of the Church of Our Savior in Christianshavn

We went to Copenhagen when our kids were 9 and 11, so slightly older than yours. They loved the harbor tour (we just took whichever one was most convenient) and seeing the Little Mermaid (she's smaller than you think she will be). They loved Tivoli, went on a bunch of rides and explored gardens. They both did their first upside down ride there which they will always remember. They also really Helsingor. We had a picnic on the breakwater next to the castle and then toured the castle.

Three more suggestions:

Supplement the harbor cruise with a trip in your own boat: http://goboat.dk/en/

The oldest amusement park in the world: Bakken. Founded in 1583

The royal guard: Go to Rosenborg and wait on the corner of Gothersgade and Rosenborggade at 11:27. Watch the guard form and see them march out of the gate on their way to Amalienborg. You can follow them all the way and see the changing of the guard in Amalienborg.

There are some open air museums near Copenhagen. If I can track down the names, I will pm you. Otherwise try google. One focuses on how Stone Age (?) Danes lived. Kids can chop wood with hatchets, go into replica huts, and paddle around in dugout canoes. The other demonstrates more modern living, perhaps 17th or 18th c., also with some hands-on activities.
I agree with the poster who said that going to Malmo just to cross the bridge is a waste of time.

As another poster noted, Mons Klint is a real pain to get to without a car. We had a lot longer in the city than you do, and ultimately chose not to do it, as beautiful as it looks. Also, we contemplated going over to Malmo, but after reflection, we recognized that we were only thinking of going to "cross another country off" our list, and decided our time would be better spent elsewhere. If those are "must sees" for you, then of course, that's your call.

If I were you, i would try to do two full days in the city itself, and then two day trips. Personally, I think one full day trip should be an early train to Helsingor for not only Kronborg, but also the excellent maritime museum (http://mfs.dk/en/, which I think your kids might really enjoy). If the weather is nice, go to Kronborg first, stop at a market and have a picnic lunch on the grounds, then go to the maritime museum, then train back to Humlebaek for the Louisiana Museum (note that Tuesday through Friday they are open until 10 p.m.).

A second excellent day trip would be to Roskilde (in fact, this is really only like a 2/3 day trip, so you'd still have time for some fun in Copenhagen). It's only about a 20-25 minute train ride from Copenhagen. Get to the cathedral in the morning (a UNESCO World Heritage Site where Danish royalty are buried), then head down to the awesome viking ship musuem (your kids will LOVE this place). Have lunch in Rosklide, then walk around the water and the park in between the cathedral and the museum. Train back to Copenhagen, you'd be there by mid-afternoon.

There is plenty to do in Copenhagen itself the other two full days you have. For the boat tour, do the Netto Badene one - it's the exact same tour as the more expensive ones. Another thing you might consider with the kids is the Exploratorium. When I went (2.5 years ago) it was in a temporary location in Christianshavn, but now it is in Hellerup. I think you'd want to see Rosenborg and its gardens. Also, a good way to burn off some of your kids' energy is to head up the Rundetaarn. Definitely Tivoli too. In Nyhavn, there is a great ice cream/waffle shop right on the canal called Vaffelbageren - grab a treat and hang out there.

Another vote for a trip to Helsingor and the Maritime Museum there. It's quite interactive; the kids can get a sailors tattoo "made" using an original ( modified)tattoo machine for example.
The Viking museum at Roskilde is wonderful too.
You can dress up in Viking clothes, and "sail" the boat, with weather sound effects.

If your son really wants to go to Sweden, you can take a very quick ferry from Helsingor to Helsingborg. (There are actually two ferry lines.) Helsingborg is a fun town to explore and there is a lovely summer palace with beautiful grounds and gardens and a play area (Sofiero) about a 10 minute drive or bus ride out of Helsingborg.

The Louisianna has a beautiful setting and beautiful grounds. It is a museum worth going to just to see the building and setting. The grounds are fairly naturalistic - lots of good running around places for children.

I thought Tivoli was absolutely magical lit up at night, though quite crowded. We went on a Friday evening in August when there was a concert. Non-concert nights are probably quieter.

I also enjoyed Roskilde, though was there in the winter so there were no boat rides.

I don't remember all the train and bus details. Our daughter lives in Malmo and she was our tour guide. If you are interested in details PM me and I will contact her.