Have 1066 go differently? William arrives before Hardrada, meaning Godwinson's forces are drained sufficiently (possibly still defeated) that Hardrada gains a foothold in the north.
Let's say that William still won in the south, so by the end of 1066 England is split. Harald holds the north-east, while William holds the south-east. Much of the west of England is still under Anglo-Saxon rule, as neither invader has extended their power westward yet.
Let's say William won much less easily TTL, and barely holds the south-east. Harald has managed to conquer as far inland as York, but still only holds the east riding and the city itself. William has made London his centre of control in England.
Wessex remains independent of the two invaders, and Edgar Atheling has been crowned King in Winchester, with Edith of Mercia, Edith of Wessex, and Godwine and Edmund Godwinson as royal advisors. Mercia is loyal to Edgar due to Edith of Mercia being Harold Godwinson's queen consort.
The Norman occupiers do not hold their conquered territory, however, and when William is killed when he puts down a large uprising in Kent, his entourage return to Normandy with his eldest son, Robert as the new duke.
Now Edgar's Wessex retakes the southeast, and Hardrada's hold on York is tentative.
At this point, Hardrada's son Magnus brings reinforcements from Scandinavia (both Norway and Denmark, which are now allied by two marriages, interestingly both involving an Ingerid.)
Norway negotiates a peace with England, and despite an uprising or two, Hardrada retains his land in England.
Decades later, the only heir to the throne of Scotland is female, and the heir to the throne of Norway marries her. Scotland is brought into the control of the Kingdom of Norway.
OR, have something happen with Canute that allows the North Sea Empire to remain stable and conquer Scotland?