Enlarged through various territorial acquisitions and conquests from Russia, Prussia, and other surrounding states, the union was first enlarged following the Ingrian War in 1617 when Finland was separated from Sweden and made a full kingdom within the union. Following Scandinavian successes in the Northern Wars of the early 1700s, Danish possessions in the Baltics were made a Duchy, autonomous within the Danish Crown, in 1720, and much of the former Prussian province of Pomerania was added to the Danish Crown in 1721.
The union was not without its internal struggles, however, as Greenland's 1814 designation as a 'crown territory' of Scandinavia demonstrated. This followed several hundred years of colonial administration in Greenland, and was at the insistence of Swedish nobles who felt that Denmark's increasing political superiority was a threat to the integrity of the union and their own relative freedom, as Denmark had originally sought to create Greenland as a territory of the Danish crown alone. This marked a turning point in the organisation of the union, moving a way from Danish superiority toward a more equal footing for all the constituent lands.
In 1849, these changes were made official with the establishment of a constitution. The constitution formalised the name of of the union as 'The Scandinavian Realm' (rather than the proposed 'United Kingdoms of Scandinavia' or the far worse 'Scandinavian Empire') at the insistence of every member of the union bar Denmark. The constitution also detailed that each member, or 'crown' as they were officially known, was to have its own parliament, with a unified parliament representing the whole realm to be based in Kalmar, the site of the original treaty signed to declare the union. The capital cities of each 'crown' were to be equal in standing, thus the Realm has no official capital (though Kalmar is often called the de facto capital). Finally, the constitution also created Estonia-Livonia and Iceland (then including the Faeroe Islands, Shetland and Orkney) as 'crowns' within the union, and Svalbard and Magen Island as 'crown territories' of the union.
In 1918, the Duchy of the Isles was separated from Iceland at the insistence of the United Kingdom, who sought protections for English speaking minorities in Orkney and Shetland. The final territorial change came in 1973, when the 4 northern provinces of Sweden and Finland were designated an 'autonomous area' within the union (though not a full 'crown') for the Sami people.
This map shows the political situation as of 2014.
Credit to Wikipedia for information, to the wonderful Fenn-O-Manic for his exemplary maps of Finland which proved a very useful reference, and to Kuusinen, who's own vision of a United Scandinavia inspired me to attempt a 'Bokmål' of my own, though his is both better and more extensive.
See also: The Kalmar Union, Scandinavia, and Scandinavism.
DISCLAIMER: This in no way represents my views on Scandinavian, Norwegian, Danish, Finnish, Estonian, Pomeranian, Icelandic or Swedish irredentism; nor any of the countries mentioned; nor irredentism as a whole. It is a work of fiction, not a political statement, and is not intended to cause offence. Please refrain from making political statements in the comments, lest you shall be subject to my wrath. That aside, comments and (constructive) criticisms are always welcome!
The labels are a Danish influenced Scandinavian Bokmål, which is kind of like a 'standard' language for Scandinavia in this time line.
...Say, you wouldn't know how to take .svg images off the Internet and put them into Inkscape and they'll still be vector images, would you? Others have tried to help, but I think it's because I have Firefox that it doesn't work. Would you know how?
If you're taking stuff off Wikipedia, you need to right click on the image make sure to 'save file' rather than 'save image' (otherwise you'll just end up with a .png or something equally unhelpful). I'm afraid that for other websites I'm not too sure as what I don't make myself, I get from Wikipedia (owing to it being copyright free), and I use Chrome, so I can't really advise you on any peculiarities of Firefox. If you still can't figure it out, I'd suggest changing your browser, even if only for downloading files to use.
Sorry for the delay in replying to this, ended up rather busy the last few days!
It it is not very common to refer to United Kingdom as "UK", but as Great Britain ("(Kongeriget) Storbritannien"), in the Nordic Countries, though it would be "Det Forenede Kongerige" in that case. "Den Russiske Føderation", or just "Russland". Also, the Crown Territory of Greenland/Iceland etc would be "Kronterritori(um)et Grønland/Island" in Norwegian and Swedish. I am a bit uncertain of the spelling in Danish, but at least in one word as in Norwegian and Swedish. "Den Statsforbund"? If it's a Polish-Lithuanian Commonwealth, it would be "Det Polsk-Litauiske Statsforbund/Statssamfunn", and I do believe you missed an "t" in "Kongeriget Prøjsen". But otherwise I am impressed by the details and by your more than passable translation into Danish.
As for the naming, you're right about it being 'Det' instead of 'Den' (which I think has been left over from when I was originally planning to have the union Swedish-lead), but the names are intended to be the 'official names' rather than common ones, hence the use of 'United Kingdom' over 'Great Britain' and so on. Everything else I'm sure you're right about, so I'll set about changing those. And I did misspell Prussia too, why do I never notice these things before I put them up?! Thankyou for your advice, it's greatly appreciated!