What a nice tradition of moving between locations.
It's a tradition that goes back to the very beginning of the DRF, even before Denmark became a nation.
Back then the king was constantly on the move through the realm.
Partly to keep in touch with what was going on and partly because before there was a formalized court system in place, the king was the ultimate judge, peacemaker and diplomat in disputes.
But first and foremost the secure the loyalty of his people. Because with a much smaller population and with a king on the move, most people had the opportunity to if not meet and address the king, then certainly to see him. They knew who he was and how he looked like - seeing and hearing him with their own eyes and ears.
It was only during the late 1400's early 1500's that Copenhagen became de facto the capital of Denmark, because by then the state administration had long since become so complex that it was virtually impossible for them to follow the king on the move.
But while the king at this time stayed for most of the time in or around Copenhagen (pretty much like now actually) he still traveled extensively through the realm several times a year.
In 1660 Absolutism was introduced. That included a set line of succession - the king is dead, long live the king. Law and order was formalized in what is known as Danish Law.
Which was based on Jutlandic Law, that at the time was at least a couple of hundred years old. That law was de facto adopted by the whole country and became known as Old Danish Law. Old Danish Law was modernized and included the whole of the Danish part of the realm. Norway, Iceland and Schleswig & Holstein had their own laws, based on Danish Law.
But just as importantly Copenhagen now became the central administration, the seat for diplomats and ambassadors and where the State Council had it's seat. It was simply the most practical thing to do. Especially in a vast realm with few and very poor roads and consisting of lots of islands and possessions overseas.
Depending on the wind and weather it could take weeks for a letter to reach Trondheim in Norway or even a couple of weeks to get to Jutland.
That means that gradually the kings stopped traveling. He had loads of local magistrates and civil servants (fogeder) to oversee the realm with their authority based (and reigned in) by law.
By the end of the Great Nordic War in 1720 the kings rarely moved away from Copenhagen.
Fredensborg was build in the 1720-30's. Located about one or two days ride from Copenhagen that was a suitable retreat and about as far away the king would travel. - And better that way, because you never knew what the wicked Swedes could come up with!
At the same time a civil servant caste had been established and they had completely taken over the control of the state apparatus and as such pretty much sidelined the kings.
Whether that was a great thing is very much debatable, but it ensured that the 1700's became one long period of peace for DK, where we really cemented our status as a leading merchant nation - a status we have to this day. DK also became much more affluent. A lot of wealth poured into the country - but there were problems. All that wealth didn't trickle down to the ordinary people. A problem that wasn't unique to Denmark!
The civil servant caste were predominantly Germans. They spoke German and their dealings was in German. Hence the saying: "I speak French with my family. German to my valet and Danish to my dog." So it was an administrative system that most ordinary Danes couldn't relate to and in most cases couldn't communicate with - and as such didn't trust.
The Danish nobility that traditionally had held administrative posts had been sidelined after 1660, with good reason! The kings simply didn't trust them to act in the interests of the realm rather than themselves. So German administrators recruited from the middle class were preferable.
Struensee, as you may recall from the movie, started a series of reforms, that were later pretty much implemented by the administration after his execution. These were much needed reforms, that also took the ordinary people into consideration. - Had we had a long hot summer with a bad harvest too, with an absent king and nobility, guillotines might have been set up in Copenhagen as well, who knows.
Then came the Napoleonic Wars and Denmark became very reluctantly and only after Copenhagen had been bombarded in 1807 involved. - On the loosing side...
Norway was lost. The state went bankrupt in 1814. Schleswig Holstein became even more oriented towards to the south and the myriad of German principalities there. This is where the action was.
The kings started traveling the now much reduced realm again, to see and be seen. To stay relevant. - Not that much traveling though but it was a beginning. At the same time Denmark became a totalitarian state. Not a dictatorship as such, but it certainly was ruled by an iron fist. That was in line with most monarchies at the time. The Napoleonic Wars had started a surge of nationalism and most kingdoms included several ethnic groups, even nations. That simmering sense of nationalism culminated in a series of revolutions, risings and rebellions during the 1840's especially around 1848. It was a chain reaction that also reached Denmark and started the First Schleswigan War.
When the Second Schleswigan War ended in 1864, Denmark was a small insignificant country with a broken spirit, traumatized.
It was time to rebuild. To rekindle the tribal spirit, to be Danish!
That meant that the king became a genuine national symbol and to stay relevant and maintain an affiliation with the various parts of the realm, they started moving around again. There weren't that many suitable royal residences around though. None actually. So the royal yacht Dannebrog was build and thus started the summer cruises.
The first Dannebrog was a paddle-steamer until it was replaced by the current Dannebrog in 1934 and as you know she is still sailing.
At the same time Marselisborg was build and finished around 1910 and used as a summer residence for the CP-family, later King Christian X.
The northern part of Schlesvig was reunited with Denmark in 1920 and became Slesvig and here the DRF took up residence at Gråsten, right at the border, because who knows when the Germans would come again...
There was also a trendy little residence at Skagen, the fashionable northern tip of Denmark, as well as the Trend Hunting Lodge.
So the DRF "gypsied" between Amalienborg, Fredensborg, Gråsten, Marselsborg, Trend and Skagen - the poor things! Not to mention the annual summer cruises aboard Danneborg.
And that's what they have been doing for the past 100+ years.