A different version perhaps...
1065 The news reached Harold and his son Olaf of Norway before winter. They spent the Yule at many gatherings and feasts, trying to gain support for an invasion into England. They reach the coast of England early spring, do no pillaging and go to a meeting with the saxon nobles. Olaf I is accepted as he has the best claim to the throne.
1066 The year of fate... William the Conquerer (was born before the POD, but I intend to go by the chaos theory idea, and after about 20 years there won´t be any players that did exist also in OTL) A distant cousin of the former king Harold decides to do absolutely nothing for now. He has recently conquered Brittony and focuses now mostly at the French power struggle. This will eventually lead to the Norman dynasty of France
1067 Olaf I of England (Olaf the norwegian as he´d become known) arrives to Denmark. He appoints Harold Godwynsson, a saxon noble man that was very revered by the former king Harold Knutsson, to become Jarl of Denmark.
1068 Harold Godwynsson marries to Olaf I sister Asrid. There is a rebellion in Denmark again but it is quelched.
1069 Harold Harthrada dies and Olaf becomes king of England, Norway and Denmark. Once again the kingdom of Knut the great is united.
1070 Olaf and Emma get a daughter, they name her Asrid.
1072 Olaf and Emma get another daughter, they name her Sigrid.
1074 Olaf and Emma get a son, sadly he is not breathing after the birth.
1075 Olaf and Emma get yet another daughter, Gudrid. Olaf finds this troubling, (unlike OTL guys like Henry VIII his claim to the English throne stems from his wife and without her he is basicly just a Norwegian pirate) on the other hand Jarl Harold and Asrid seem to be doing fine in producing heirs. Their son Knut seems to healthy, strong and bright.
1076 Olaf notices that the Jarl of Orkneys, Erlend has become increasingly powerful in Scotland. He has in fact gained so much land there he doesn´t need much more to swallow it up and become king. All he needs is just support from the chieftains of Scotland. Olaf invites him to London for Yule and is assured by the Jarl, that he has no ambition to become king of Scotland. They drink a lot together and the Jarl reminds the king that they are both Norwegian. Olaf and Erlend agree that Asrid the oldest daughter of the king shall marry the Jarl´s oldest son Rognvald (Rögnvaldur).
1077 Olaf visits Denmark and Harold Godwynsson. He spends the Yule there before going north to Norway. He returns home after assuring the norwegians that he is still one of them, despite having raised taxes a little bit.
1078 A messenger from Norway reaches Iceland and offers Iceland the protection from the king of Norway, England, Denmark and the Orkneys. Many Icelanders feel they should accept the offer. After all most young men go now to the court of either Harold Godwynsson in Denmark, Erlend of Orkney´s or to Olaf in England, and all the trade Iceland has with the rest of the world is with the kingdom of Olaf, (except for a little trade in Ireland). However as Olaf hasn´t threatened them with anything those who want remain independent still have the majority although all realize that if the king decides that they´re his, they really don´t have a choice.
1080 Finally the pope gives his verdict. The archbishop of Bremen is not the archbishop of the north. England is obviously the one that converted the north. England converted king Knut the great, England converted the Norwegians and the Danes, and the Norwegians converted the Icelanders and Greenlanders.
The Archbishop of York presides over Denmark. The bishop of Lund is under him. He also presides over the Bishop of Norway and the Icelandic bishop of Skalholt.
1081-1083 The scottish wars. Erlend of the Orkney´s conquers Scotland with help from king Olaf´s army. He becomes the Jarl of Scotland. (This is not the end of free Scotland though)
1084 Harold Godwynson returns to England, he doesn´t go immediatly to see the king. In fact he has taken his son along with him and is trying see how much support he could get to become king after Olaf. He visits Olaf eventually and spends the Yule with him. He tries to remind Olaf that back in 77 he promised to declare Knut his heir. Olaf assures him he has not forgotten.
1085 Harold announces in Denmark that Knut will inherit the crown of England. The Danes are happy because although Harold is English and Asrid norwegian, they view Knut as a dane, first of all the name helps, but also the fact that he has spent his hole life in Denmark and his father has governed wisely. They view Knut as a possible return of power to Denmark.
1086 When Erlend hears the news of this he is furious. Has Olaf forgotten his promise. Erlend realizes that he has problems if he intends to put his son Rognvald on the throne. First of all his men could be tied up if the Scottish rebel. Secondly, Harold Godwynsson has strong support in Denmark, and strong support in England. Rognvaldur on the other hand has stronger support in Norway and a more direct claim to the throne, that is if he gets married to Asrid.
1087 Rognvaldur and Asrid marry. Olaf I announces that Rognvaldur shall inherit the kingdom after his death. This results in a lot of: "What? What? WHAT?" from English and Danish nobility. Some talk about that the Norwegian is over-extending his welcome.
1088 The Archbishop of York joins the Saxon discontent by claiming that Rognvaldur cannot become king as his father is an illegimate bastard child. This angers Olaf I and he rides to see the Arch bishop along with his army. He intends to use force to make the Arch bishop change his claim. It works but it outrages the nobility of England even more.
1089 The nobles rebel against Olaf. The soldiers that remain loyal to Olaf are to few to counter the force of the rebels. Basicly just the Norwegians and Icelanders stick to him, while the Saxons and Danes tell him to stick it. Olaf is defeated and is made to sign a declaration. The king shall not be able to assign an heir without the consent of a council of English and Danish noblemen. He is also forced to accept Knut Haroldsson as his heir.
Of course Erlend and Rognvaldur are bound to do something...