|Ælfgifu on the Bayeaux Tapestry|
Svein Forkbeard died in 1014, and our old friend Æthelred the Unready moved in, forcing Cnut to flee to Denmark. While there, Cnut and Ælfgifu had another child who would grow up to be Harold Harefoot (King of England from 1035-1040, and mentioned here).
In 1016, Cnut re-conquered England, and then cemented his power base there by putting Ælfgifu aside and marrying the widow of Æthelred, Emma of Normandy. This doesn't mean that his first wife was completely removed from power: he sent her to Norway with young Svein where she apparently ruled while acting as regent for their son. This period in Norway is remembered for heavy taxes and shortages.
Back in England, Cnut's death in 1035 created a conflict. Cnut and Emma had a son, Harthacnut, who was next in line. Ælfgifu wanted the throne for her son Harold, and probably made a lot of the decisions during his five-year reign. Harold died in March of 1040 and was buried at Westminster Abbey. Harthacnut at the time was preparing to launch an attack on England; he was able to just step in, take the throne, and have Harold's body dug up and thrown into a swamp. (Loyal followers later found it and buried it again.)
After 1040, the woman married to one king and mother to two more fails to show up in any records.
*She was called "Ælfgifu of Northampton" in the Anglo-Saxon Chronicle to distinguish her from other Ælfgifus, such as those of Exeter, York, and Shaftesbury; it was a popular name!