OK, so skipping the details about the Spanish War of Succession with Swedish and Polish input for now, let's just say the following happens:
During the War of Spanish Succession, Charles XII begins to hear hear stories filtered through his generals of the British and Dutch ship captains' trade with the New World and the East Indies and he becomes convinced that Sweden needed to expand its navy beyond the Baltic Sea.
To this end, he marries princess Sophia Hedwig of Denmark in the hopes of reducing or nullifying the Sound Toll for Swedish product going through the Øresund on non-Swedish ships but the Danes are intractable. Thus Gothenburg, started by Gustavus Adlophus a hundred years before, becomes his goal. Nominally Swedish ships built in Gothenburg from local timber but paid for and by crewed by Dutch and Scottish companies start exporting products from Livonia, Ingria, Pskov, Finland and Novgorod, plus importing in the reverse direction. Being nominally Swedish they use Sweden's exemption from the Danish Sound Tax under the Copenhagen Treaty of 1660 whenever they cannot stay close to the Swedish Coast and away from the Danish fort of Helsingør and its guns. Even though Sweden collects their own tolls, they are less than the Danish tolls so Dutch and British commerce begins to preferentially use the convenience of the Swedish flag.
This angers the Danish crown, who depend upon the tolls paid by the Dutch and British ships for much of their income. When Denmark announces that as of January 1st, 1718 they are rescinding Sweden's exemption from the Sound Toll, Charles XII declares this an abrogation of the Treaty of Travendal in 1700 which committed Denmark to upholding all previous Dano-Swedish treaties and demands that the exmption be reinstated. The Dutch- and British-owned ships flying under the Swedish flag continue to stick close to the Swedish coast to avoid the toll. On March 7th a Scottish-crewed ship is sunk by the Danish at Helsingør but some crew make it to Helsingborg in Sweden and on the 9th Charles XII declares war and requests the Travendal guarantors swift action in support. First the Swedish Navy, which has been built up over the last decade and trained by Dutch and British captains, only ferries troops into northern Jutland as well as backing up their Holstein-Gottop allies who attack from the south, but on November the 1st the bombardment of Copenhagen begins after all Holstein and much of Jutland and Schleswig were under Swedish control. It, however is just a distraction as Charles XII shows once again his military brilliance by sailing from Gothenburg up the Frederikssund and disgorging his army in Roskilde on November the 2nd. Because the Danes are expecting the Swedish attack to come from across the Øresund from behind the bombardment, Charles XII's "attack from behind" is a near complete surprise resulting in the collapse of the Danish forces.
Frederick IV of Denmark and his family escape in the confusion past the Swedish troops and attempt to make it to Iceland by sea. The ship's rigging is damaged by a lucky cannon shot at night but still manages to escape to the North Sea. There, they encounter a British Naval vessel which offers to help guide them to Edinburgh after they claim they are a Swedish trade ship beset upon by Danes. Several of the British sailors, though, had worked on merchant ships run out of Gothenburg and knew the difference between Danish and Swedish accents and alerted their officers. The British, as guarantors of Travendal, had been looking for something like this once it had become apparent that the Danish royal family had disappeared. The ship is escorted to Edinburgh, supposedly as teh British ship was heading there themselves for resupply and would be more than happy to make sure the Swedish ship with its damaged rigging would get their since they had though their were closing in on London. When the two ships arrived at Edinburgh, the royal family was confronted and placed "under diplomatic protection" before eventually ending up in the Tower of London palace.
Meanwhile, Charles XII clais the throne of Denmark through his mother, Ulrike Eleonara, who was the daughter of Frederick III of Denmark and aunt to Frederick IV. When the diplomatic arrest of the Danish royal family is made known a month later, Charles demands that the Travendal guarantors uphold his claim to the Danish throne as the closest male relative after Frederick's brother, the withdrawn bachelor Prince Charles, who escaped with his brother's household.
The United Provinces upholds Charles XII's claim to the Danish throne for commercial reasons and George I of Great Britain follows suit after Charles XII promises a stipend for Frederick IV's family if they renounce all claims to the Danish throne. Frederick IV holds out hope for return into 1720 as sporadic fighting continues to erupt across Jutland but the peace slowly returns after Charles XII extends the taxation and legal reforms he implemented in Sweden to Denmark and Norway, which are well received.
On finally receiving word of Frederick IV's capitulation in June of 1720, Charles XII is crowned as "King of Sweden, Denmark and Norway, Grand Prince of Finland, Duke of Ingria, Estonia, Livonia, Schleswig, Holstein and Pomerania, Prince of Pskov and Novgorod" on July 1st, 1720, in Stockholm, and over the next six months in the local capitals of each of those realms.
If this is what you're going for, I'm afraid I'll have to call it out as too much of a Caroluboo-wank and say that it crosses into ASB-territory.
You don't build up a capable navy in just a couple of years. It takes decades. And the Swedish Navy in the 17th and 18th centuries was incapable of doing anything right, so in a war against Denmark they would have to rely on British, French and Dutch support - just like they did in 1700. The British, French and Dutch, however, only supported Sweden in 1700 because they were afraid of Denmark defeating Sweden and gaining the upper hand in the Baltic. In a scenario such as this one, they wouldn't support Sweden, since they're just as wary of Sweden gaining the upper hand (1658) as Denmark (1679, 1700). One country annexing the other is out of the question.
Besides, how does Charles accomplish all this? You give credit to his military brilliance, but really he wasn't all that great. It was the skill of his soldiers, a result of his father's military reforms, that won him his battles, not his tactics. The Swedish Navy and its leadership was extremely incompetent whilst the Danish Navy has always been the strongest, best led and best organized part of the Danish military, so the Swedish Navy just outmaneuvering the Danish Navy at every turn won't happen. Neither would it be possible for Sweden to navigate through the narrow Danish straits (the Danish Navy, if I remember correctly, possessed top-secret, highly detailed and accurate maps of the country, meaning the Danish Navy would always have a huge advantage should an enemy power try to wrest control of the straits), let alone a narrow fjord. If the Swedish Navy tried to sail into Roskilde Fjord it would get annihilated, it would be suicide. A slight wind would ground their ships, a couple of batteries could sink them, and I'm not even sure the fjord is deep enough for larger ships to sail there. Besides, how would they land a force large enough (in one go, in your story they have the element of surprise) to match, not to mention defeat, the Danish armies? How would they do it through such narrow waters? How would they keep them supplied? This is a 18th century Sealion, sorry.
The Swedish Army wouldn't be able to overrun Denmark in a matter of months. There are several large fortifications to contest with, and the ice has melted long ago. Copenhagen was one of strongest fortified cities in Europe, taking it would be very hard.
Lastly, why does the Danes and Norwegians just accept that this autistic Swedish warmonger now rules their countries? Nationalism developed very early on in Denmark, and invading Swedish armies always had to contend with Danish guerillas - snapphaner and friskytter. One example of this early nationalism can be seen on Bornholm in 1658; the Danish population rebelled, killed the Swedish governor and swore allegiance to the Danish King. When Charles X Gustav stood outside Copenhagen in 1658, he tried to convince the Danes that it didn't matter whether they were ruled by Danes or Swedes.
"What difference does it make whether it's King Frederick or King Charles?" he would ask. He didn't win any support because there was a fierce hatred between Danes and Swedes. Danes would never sit by and silently accept Swedish rule, nor would the Swedes accept Danish rule.
And what about Norway? Norway is a tough nut to crack with its harsh winters and many mountains. Invading it would prove arduous, just like it did in real life: It cost Charles his life and it destroyed the remnants of the Carolean army. Even if Denmark should fall, Norway would fight on, you can be sure of that. If the royal family were to evacuate, it would be to Norway and not Iceland. In 1658, when it looked like Denmark might be wiped off the map of Europe, there were actually plans for the royal family to evacuate to, and continue the fight from, Norway. The idea of Charles magically defeating Denmark in a matter of months and then just acquiring Norway in the peace deal is ludicrous.
I like the idea of the TL, but just watch out it doesn't become a wank.