If not what is the closest country to this? Even if a country planned to conquer these part or all of these it would be helpful. Thanks
There was in fact more closer candidate in medieval Scandinavian history - so-called Norwegian Dominion (Norgesveldi) in making, colonies of former independent Norse-speaking people now ruled by the king of Norway around 1260.
As I briefly mentioned before in: How did the Faroe Islands get into the hands of the Kingdom of Denmark? Is it a colony or constituted as something else?, this "Norwegian Dominion" was indeed a historical precursor of the North Atlantic dominion of the Kalmar Union - the latter inherited island colonies from the king of Norway.
While Icelanders officially acknowledged their subjugation to the crown of Norway in 1262/63 just as Greenlanders did, King Håkon (IV) Håkonsson of Norway (d. 1263) tried to secure his political influence over local rulers in western seaways in Scotland as well as in the Irish Sea against the king Alexander III of Scotland in his last days, but he died in the Orkney Isles on the way of the expedition.
Håkon's son and successor, King Magnus Lagabøte (the Law-Mender, d. 1280), however, concluded a treaty of Perth with King Alexander of Scotland, by deciding an official cession of the disputed Norwegian lordship over the Isle of Man and Hebrides in exchange of some annual payment.
How the king of Norway had built their political influence over the Northern and Western Isles of Scotland (down to the Isle of Man) had a long history, at least dating back to the 11th century, and two expeditions conducted by King Magnus Barelegs (d. 1103) is said to have been a turning point.
The king of Norway sometimes landed the Orkney Isles on their way of expedition as a bridgehead of their political and military presence in the fringe area of the British Isles even beyond the alleged end of the Viking Age - as King Harald hardråde did before his end at the Battle of Stamford Bridge in northern England in 1066 and his grandson, King Magnus also did twice around 1100. As his grandfather had been, King Magnus also met his end in expedition in northern Ireland in 1103 - according to later tradition, he was said to try to conquer Ireland by force as well as the alliance with "the king of the Irish". According to a British (Welsh) text, the fleet of King Harald (though he did not lead the fleet by himself them) had also been active in the Irish Sea in 1058. The political influence (overlordship) over the "Insular Viking Zone" (Etchingham 2001), the westward route of sea stretching from Norway into the Irish Sea, was certainly a sometimes pursued political goal for the king of Norway from the 11th to the 13th century.
While the earl (jarl) of the Orkney did not try to integrate Iceland, the earldom of the Orkney, especially under the reign of Earl Thorfinn's father, Earl Sigurd the Stout (d. 1014), sometimes consolidated their political influence extending well into the Irish Sea. Earl Sigurd also met his end in the battle field of Clontarf in Ireland in 1014, allying with King Sithric Silkenbeard of Dublin against the army of King Brian Boru.
After the death of Earl Thorfinn (the Mighty, d. 1065), once independent earldom of the Orkney Isles were often divided by the succession strife and prone to the external intervention (either from the king of Scotland (Alba) as well as the king/ throne contender of Norway), but it was not until 1195 that Earl Harald Maddadsson (d. 1206) finally submitted himself to King Sverre of Norway and lost the lordship over Shetland after his alleged involvement with rebellion and its defeat.
12th century Orkney also enjoyed wide and active cultural interactions with neighboring Norse-Gael powers - both Earl Rognvard Kari Kolsson (Half-Orcadian & Norwegian) (d. 1158) and Bishop Bjarni Kolbeinsson (d. 1223) were renowned Old Norse vernacular poets (skalds), whose arts blossomed once again especially in the late 12th and 13th century Iceland by the hands of famous Icelandic poets like Snorri Sturluson (d. 1241).
So, based on these historical as well as cultural tradition, Earldom of the Orkney Isles itself can also be a kind of dark-horse to OP's question, I suppose.
References:
Your best bets are likely either the Kalmar Union (1397-1523) or, the North Sea Empire (1013-1042). Though there are problems with both, namely that neither directly “controlled” Iceland, Scotland, or Ireland all at once. A lot of this has to do with the fact that for a very long time, none of those places existed as sovereign or united countries, and their borders were hazy at best.
For some backstory, the Kalmar Union was a non-continuous union of Denmark, Sweden, and Norway. Legally the countries were all still sovereign states, though their domestic and foreign affairs were controlled by a single monarch. This union brought Iceland and Greenland, among other places, under a single ruler, as they had previously been under Danish political control. The North Sea Empire was a personal union between England, Denmark, and Sweden. The Empire was a thalassocracy dominated by Norse culture, and vikings from Denmark.
By controlling England, the North Sea Empire was able to exert considerable economic and social influence over the weaker and fragmented Scotland, and Ireland. Both places were considered backwaters in the early Medieval period. Ireland consisted mainly of city states, villages, and small kingdoms, each with their own unique identity and language. Many of these city states and small kingdoms were at the mercy of the North Sea Empire, and had been experiencing raids and various wars of conquest by Danish vikings for the last 400 years. Scotland, while technically ruled by a singular king, still experienced a high degree of factionalism. Large swaths of its southeast were also controlled by the English, and by extension, the North Sea Empire.
So while no one empire or kingdom ever fully controlled Ireland, Scotland, and Iceland all at once, both the North Sea Empire, and the Union of Kalmar came very close.