Beginning as OTL
The greatest times of Denmark (which had once ruled England under Knut the Great) were already over in 1200; still, in 1219 Denmark managed to conquer Estonia. (Legend has it that the Danish flag, the Dannebrog, fell from the sky during a battle in this year.) Its influence on Northern Germany, however, was lost in the Battle of Bornhöved, 1227.
The year 1282 became a very important one for Denmark: In this year, the nobility forced the king to grant a charter, considered Denmark's first constitution.
The position of the Danish kings started to weaken further in the 14th century: In 1326 king Christoffer II was kicked out after he wanted to tax the nobles and the church; from now on, Gerhard III of Holstein effectively ruled the country. Due to the latter's marriage to countess Margarethe of Holland, Zeeland and Hennegau in 1331, Denmark's personal union to the Netherlands was prepared. Skane was lost to Sweden in 1352. After coming of age, king Henrik II tried to subdue his vassals, especially mighty Holstein, in 1360, but was defeated and lost most power. Even worse, he had to sell Estonia to the Teutonic Order to pay his debt. Jutland now was completely under Holstein's control. Some of the king's followers fled to Bornholm in 1368 now that their cause was lost, forming the Bornholm Brotherhood, starting piracy in the Baltic.
Rise, thanks to Prince Harald and Atlantis
Since about 1350-75, due to growing demand for food, Denmark had extended fishery in the North Atlantic, going farther and farther west. Soon, tales of strange islands in the far west start to spread among fishermen and sailors.
1381, the Danish prince Harald went on a journey with some fishermen, interested in their tales of lands in the west. They landed in OTL Newfoundland (later named Haraldsland), meeting some natives. Prince Harald claimed the land in the name of the Danish king, returned to Europe together with some natives. The prince would send those bronze-skinned men to various European courts, astonishing people, which made him many influential friends - and when he would become king later, the dukes of Holstein wouldn't dare to take a move against him, as long as he reigned.
1387, Prince Harald made a second journey to America, coming as far as OTL Manhattan this time, which was named Prince-Harald-Island in his honor. A scholar who accompanied him brought an interesting new weed to Europe - the tobacco.
Denmark under the Schauenburger dynasty
In 1396, Black Death arrived in Denmark, killing a good part of the population, similar as in other European countries.
The conflict between the native Danes and the Schauenburger from Holstein started to grow. In 1406, Emperor Gerhard I was murdered by a Danish nobleman, who hated the all-powerful Germans.
This couldn't stop the Schauenburger, however: After the death of king Harald, his brother governed Denmark until the latter's nephew Erik VIII would come to age. Now however, Holy Roman Emperor Gerhard II (who already owned Jutland as a fief) conspired with the regent's younger brother, eventually taking power in Denmark for himself.
This division lead to some trouble in Atlantis. In 1438, the kings of Denmark and the Netherlands finally agreed for a compromise in the New World, negotiated by the pope: Denmark kept the northern colonies (Prince-Harald-Island, Haraldsland, New Jutland), which were extended with time over the whole OTL Canadian Maritimes and the Hudson valley. The Netherlands got the Southern colony of Nieuw Zeeland and were allowed to colonize the lands further south.
On his second journey in 1471, he discovered the mouth of St Lawrence river, but was killed a bit later by Atlanteans, so the expedition decided to return.
In 1475, another Danish expedition reached Lake Ontario. Soon, the first Danish colonies along St Lawrence river were founded. Together with the colonies of Prince-Harald-Island and Anderland, they formed a belt around the English colonies.
Denmark suffered a heavy setback in the anti-Danish War 1509-12: After some clashes with Danish colonists in Atlantis, the Quadruple Monarchy declared war against Denmark and also won the Dutch as allies. In the peace of Hamburg, Denmark lost its lands in OTL Canada to the Quadruple Monarchy and Anderland to the Netherlands. Only the city of Haraldsborg (OTL New York, plus Long Island) and Prince-Haralds-Land stayed in their hands. And even Haraldsborg was lost in 1544 to Poland.
In 1520, the nobles of Sweden decide to make Henrik VI new king, since the regent Knut Karlsson of the Bonde family had no heir. 1523, Henrik was also elected new king of Norway, now reigning all of Scandinavia.
When the united Scandinavia started the Sund toll, the Hanseatic League clashed with the former. This time, the Hanse cities lost the war from 1521-23.
1535, King Henrik VI started the Scandinavian church, confiscated the church property and had the bible translated. But only a few years later, everything fell apart when in 1541 his son Gert II was deposed for complete madness. Norway became a nobles' republic again, Sweden declared independence too. Denmark itself fell into Civil War, with various (wannabe) contenders fighting. The war was only ended in 1555 by Alexander / Alasdair IV of Scotland and Ireland, who was also elected king of Norway and Sweden (in 1562 and 1567 respectively).
After the death of Alasdair in 1588, his vast lands were divided: Scotland and Ireland went to his elder son Alexander / Alasdair V, Scandinavia to his younger son Christian / Kristian I. But as early as 1595, the nobles of Sweden deposed king Kristian after the lost war against Vladimir (1592-94), and elected Albrecht / Albert of Mecklenburg new king. Norway stayed Danish however, although it was shorn of Göteborg, Trondheim and Narvik after the First Nordic War (1607-11).
Unification with Braunschweig
In 1628, Kristian I died without heirs, and the nobles decided to make duke Ernst V of Braunschweig-Lüneburg new king. About this time, Denmark started to approximate France diplomatically. They fought on France's side against the Dutch in the Anti-Dutch War 1630-35, gaining Nieuw-Nederland in the peace of Bremen; and in 1637, they supported the Dissenter's Revolt in New England, getting Haraldsborg back and became protectors of the Commonwealth of New England. After king Humphrey I of England had won the War of the 'fords and accepted the loyalty of markland, he tried to regain New England; but Denmark-Braunschweig allied with Florence in the Atlantean Coalition and won surprisingly.
1634, king, duke and elector Ernst V died without a son, making his daughter Margarethe new queen.
Denmark fought on France's side in the anti-French War; the war was mostly fought against Sweden, which is why this war is also called "second Nordic War". In the Peace of Amsterdam 1694, Denmark lost all of norway to Sweden, but received a big part of formerly French Louisiane in Atlantis. Soon, German settlers went into these new lands; 1746-50, they had to fight the French-Atlantean War.
1709, mad King Kristian III of Denmark was killed by court members after trying to force the church to canonize him while alive.
In the French Republican Wars, Denmark fought for the cause of monarchy; but in the third French Republican War, this would lead to their downfall, when Sweden-Norway allied with France and conquered all of Denmark.