Copenhagen-Billund-Germany

I don't have any tips for Denmark, but if Hamburg is too modern for you, you should definitely go to Lübeck. Lübeck looks back on a very long and interesting history as the Queen of the Hanseatic Cities. From there, you can definitely take trips to Schwerin, Hamburg, or other smaller towns.

There's a lot more to Denmark than Copenhagen and Lego.
Four days seems like a LOT for Billund, while 3 seems skimpy for Copenhagen.
Aarhus, Denmark's second city, has several sights that are interesting for the young ones: rainbow bridge at the modern art museum; bog bodies in the archeology museum; DOKK-1 with its automated parking garage; another Tivoli.
If you go all the way up to Skagen, you can walk out on a long sand bar and see where two seas meet.
All over Denmark you can hunt for Thomas Dambo's trolls. https://www.thomasdambo.com Some can be seen by bike in and around Copenhagen.
One of the southern islands (Langeland) has wild horses.
Gisselfeld has a park with a 16th century castle, fancy garden and a treetop walk. https://www.gisselfeld-kloster.dk/Hjem.aspx?lang=en-gb Holiday homes for rent in the huge park.

Hi,

4 days is a long time in Billund. To be fair, it has Legoland, Lego House and Lalandia - but it's still a small town with less than 8,000 inhabitants. Don't spend more time in Billund than you'll need for the top attractions. Copenhagen is much bigger and have a lot to offer, including many easy daytrips, so you can EASILY spend more than 3 days here without getting bored.

Is this a doable trip via train?

It's absolutely doable by public transport. There are no trains to Billund, but one easy transfer onto a bus is all that's needed.

Does this order make sense?

Yes, it does.

Should we stop on the way to Billund at any other cities?

You could stop in Odense for H. C. Andersen's House.

What are we missing in Denmark?

You are missing a lot. I want to repeat what G3rryCee says above: "there's a lot more to Denmark than Copenhagen and Lego" - way too much more to list here. Rick Steves have some inspiration, so does Visit Denmark. Maybe it's okay to miss a lot, you can't feasibly do it all on a two week trip - especially if you (understandably) want to experience Germany/Belgium/the Netherlands too. I think you'll have to choose between Denmark in (more) depth or visiting other countries too.

Quick comments: It's good that you have Copenhagen on your list. It has a lot to offer and something for everyone. Billund is (from my perspective) more for the kids, which sounds very suitable for your family. Aarhus is a good contender, though I'm not excited about Tivoli Friheden (in Aarhus, not to be confused with Tivoli in Copenhagen), but will highlight places such as Den Gamle By instead.

We are planning on taking 2 weeks and have played with the idea of adding on Brussels or Amsterdam - but that seems like it may be too much.

Maybe it's a bit of a stretch, unless you either fly from Billund (yes, it has an airport too) or choose a German city naturally on the way, such as Hamburg, Bremen or Köln (though my experience with these cities is not exhaustive).

On our recent trip to Denmark, we (two adults) spent two nights in Ribe. There's a Viking "living history" kind of place nearby that we enjoyed. I saw brochures for another Viking place that (if I recall correctly) was near Billund. Your kids might enjoy something like that - my kids would have at that age! We also rented bikes from a local shop and biked over to the coast. You could look into staying somewhere along a coast if your family enjoys that kind of exploration. You could also consider Roskilde near Copenhagen - there's a viking ship museum which was quite fascinating, and also had a shed where kids could build their own ship out of scraps of wood.

Last year we had two of our young adult kids with us, and were going from Copenhagen to Amsterdam. I initially considered taking a train but it was going to take a whole day and they were only with us for one week, so we opted to fly instead. This year we took a train from Ribe to the Netherlands; the Ribe to Hamburg part itself required something like 5 transfers although they were all quite easy. I suspect Billund to Hamburg would be similar.

Is this a doable trip via train? Does this order make sense?

Both yes.

Should we stop on the way to Billund at any other cities?

Depends on interests. Odense is an option or castle Egeskov Slot or World Heritage Jelling Monumenterne.

Where in Germany should we go? This is a first time in this part of Europe for all of us and we'd like to see Germany while we are in the region. I was looking at Hamburg, while beautiful seemed a little more modern that we would like.

Hamburg was brutally bombed out in WWII. Alternatives also depend on interests: Viking museum village Haithabu and Gottorf Castle are on your way to Hamburg. Lübeck's World Heritage old town is a day trip from Hamburg - history buffs shall visit Museum of Hanseatic League which rules parts of Europe nearly 500 years. A smaller nice town one is Stade. Schwerin has nice old town elements and a beautiful castle which is still in use by a state parliament.

What are we missing in Denmark?

Really a lot because Denmark has so much to offer but some things need a car, e. g. animal park Givskud Zoo where you can drive nearby lions. Rive was mentioned, Rømø island and beaches, Aarhus with "den Gamle By", Northern Jutland, a museum sailing war ship, Hanstholm bunker museum, Tirpitz bunker Museum, some nice harbors and castles and lighthouses, Christiansfeld (World Heritage), Lillebælt bridge walking, Ærø ... just to name a few. Fjord&Bælt on Fyn would be nice for the kids.

In Germany places such as U-995 (WWII submarine), Flensburg brewery and other places would be also northern of Hamburg - plus one of the best bakeries I know.

One thing you cannot visit but which is really unique in the world is the history part of Schleswig plebiscites from 1920 which still has noticeable consequences today.

I recommend to leave Brussels, (Bruges) and Amsterdam for another journey.

I saw brochures for another Viking place that (if I recall correctly) was near Billund.

The brochure might been of Bork Vikingehavn. It's about the same distance from Billund as Ribe Vikingcenter. Easy to reach by car, not so much by public transport. Haven't been myself. But there's also Kongernes Jelling, much close to Billund, that is however not "living history" and far more a "classic museum" (though a fairly decent one at that, I'd say).

the Ribe to Hamburg part itself required something like 5 transfers although they were all quite easy. I suspect Billund to Hamburg would be similar.

Normally Ribe - Hamburg would be two transfers, so sounds like you must have travelled during track works or other disruptions. Billund - Hamburg can be completed with just one transfer.

Another Viking site near Schleswig, Germany. https://haithabu.de/en/about-the-viking-museum-haithabu

Schleswig is on a train route between Copenhagen and Hamburg although the Viking museum is in a rural area so a car would facilitate visiting.

As Mark mentions above, Schleswig Holstein has a lot to see. Don’t look for info from Rick Steves. He ignores the area.

Transport between Billund and Copenhagen is 1 train and 1 bus (between Vejle and Billund). Total transit is a little over 3 hours with the bus portion 30-40 minutes. I'm pretty sure options leave every hour for this itinerary, but I'm planning on traveling in the opposite direction, so timings may vary for you.

My family hasn't been yet, but I have done a lot of research so far. We plan to stay 3 nights and have 2.5 full days in Billund. One full day for Legoland and one for Lego House. The other very popular attraction in the town is Lalandia, which has a ton of activities but is principally known for the indoor water park. We plan on skipping Lalandia, but I can see that taking another day if you wish. Other than those 3 things, there really isn't much to do, especially if you don't have a car. IMO, I'd limit your time in Billund according to how many of the "big 3" activities you want to visit, and maximize your time in Copenhagen. Through my planning and research, there seems to be a lot of activities in Copenhagen that kids can enjoy.

Normally Ribe - Hamburg would be two transfers, so sounds like you must have travelled during track works or other disruptions.

Oh you're right, I checked my journal: Ribe -> Bramming -> Kolding -> Hamburg.
But then we had transfers in Münster and Oberhausen and finally had to get on a bus to get to Arnhem because of some issue (with the track? the train? I did not hear the announcement properly and only realized we had to get off when I noticed the train was completely empty... luckily we didn't miss the bus as a result...) We also missed one transfer because of a delay (Münster maybe?) It was a long day! But we did have a wonderful dinner in Arnhem before getting on yet another bus to our accommodation...