November 12, 1035. Cnut dies
Assembly at Oxford: "joint rule" of Cnut's sons Harthacnut and Harold Harefoot
The Chronicle notes that at Cnut's death there was a divided succession. The two candidates were Harthacnut, the son of Cnut and Emma, who was then ruling in Denmark, and Harold, apparently a son of Cnut and Ælfgifu of Northampton, an earl's daughter, though the Chronicle records doubts about Harold's parentage. At an assembly at Oxford, Earl Leofric of Mercia and most of the nobles north of the Thames (the Mercians and Northumbrians) and the shipmen of London wanted Harold to rule, as a regent for himself and his absent brother Harthacnut. Earl Godwine of Wessex and the nobles of Wessex opposed this as long as they could, because they wanted Harthacnut to succeed, but could not prevent it. It was determined that Emma should stay in Winchester with Harthacnut's housecarls and keep Wessex for Harthacnut, and Godwine was her most loyal supporter. However, the Chronicle continues, Harold was full king over all England, and he had seized many of Emma's treasures into the bargain.
1036 (?). Emma switches allegiance from Harthacnut to the æthelings in Normandy
Godwine switches allegiance from Harthacnut to Harold
Edward and Alfred return to England; Edward repulsed at Southampton, Alfred captured
February 5, 1037. Alfred, Æthelred's son, dies at Ely
Things might have been very different if Harthacnut had returned to England immediately after Cnut's death in 1035. Unfortunately, Harthacnut's position in Denmark was threatened by Magnus of Norway, and he did not in the end leave until 1039. It seems that Harthacnut's continued absence made Emma realise her position as regent for Harthacnut (her son by Cnut) was untenable, and so she shifted her allegiance to Edward and Alfred (her sons by Æthelred), inviting them to return to England. This however would be a threat to Godwine, who owed his position to Cnut's favour and might expect less advancement under a son of the previous ruler than under Cnut's son Harthacnut, so Godwine seems to have shifted his allegiance to Harold.
The reasoning is conjecture, but both Edward and Alfred did return from Normandy to England in 1036. Edward's return is not recorded in English sources, but Norman sources note that he arrived at Southampton with a (Norman) fleet of forty ships, and was repulsed (presumably by English forces loyal to Harthacnut or Harold), and returned quickly to Normandy. Alfred, according to one version of the Chronicle, came to the country wanting to visit his mother in Winchester, but Godwine would not allow it, because feeling was veering towards Harold. Godwine captured Alfred, killed most of his companions in gruesome ways, blinded Alfred and set him down at Ely, where he dwelt until he died. (One manuscript of the Chronicle is written from a pro-Godwine viewpoint, and does not mention the death of Alfred at all.)
The Chronicle's note that feeling was veering towards Harold, "although that was not right", is corroborated by a letter written in July or August 1036 from one continental cleric to another, which mentions reports from English messengers to Harthacnut's sister Gunnhild, that Ælfgifu of Northampton and her son Harold are trying to corrupt the English by entreaty and bribery so that they will swear oaths to support Harold, and that one of the nobles so approached was so incensed that he sent messengers off to Harthacnut, urging him to return quickly. The process of the suborning of the southwest can also be followed in the coinage. In the first year of the joint rule (1035-6), coins were being minted in the name of Harthacnut south of the Thames (i.e. in Wessex), and in the name of Harold north of the Thames (i.e. in Mercia and Northumbria), with mints on the Thames operating apparently for both Harold and Harthacnut. However, over the course of the second year of the joint rule (1036-7), more and more of the coinage was being issued in Harold's name, and mints south of the Thames (in "Harthacnut's" territory) also began operating for Harold. It was perhaps the beginnings of this process that convinced both Emma and Godwine that waiting for Harthacnut was a losing tactic, and more desperate measures were needed.
S. Keynes, "Introduction to the 1998 Reprint" of Alistair Campbell (ed.), Encomium Emmae Reginae (Cambridge: 1998), at pp.xxx-xxxiv
1037. Harold Harefoot becomes king of all England
With the Norman æthelings killed or repulsed and Harthacnut still away in Denmark, Harold was finally chosen as king over the whole country, and Emma was driven into exile, and fetched up at the court of Count Baldwin of Flanders.
March 17, 1040. Death of Harold Harefoot
Harthacnut becomes king of all England
When Harold died, the English counsellors sent to Flanders for Harthacnut, and he returned to rule England, with his mother Emma. The Chronicle has nothing good to say about his reign, noting that he started by imposing a very severe tax, and went on to have the body of his dead half-brother Harold dug up and thrown into a fen. His ravaging of Worcestershire the following year (q.v.) cannot have increased his popularity, nor his betrayal of a safe-conduct that same year, and it was probably in order to protect his reign from open revolt that he invited Edward the Confessor to return from Normandy and share the rule with him (q.v.). Shortly after this (in 1041/2) the Encomium Emmae Reginae was commissioned and written, as another strand of a campaign to engage public support and sympathy for Emma and Harthacnut.