In 18 of September of 1066, the Norwegian king Harald lands on the beaches of Scarborough and began his invasion of England, in September 25 Norway lost the battle of Stamford Bridge and retreat to Yorkshire, 3 days later the Normands land in England, in 14 October the 2 armies confront themselves in Hastings remaining far from combat. In 4 December The English King and the Normand Duke agree on a ceasefire after moths of starving and dead from the 2 sides...
Rodrig3D
If I read you correctly Harald is defeated at Stamford Bridge but without his death or the virtual total destruction of his army? Also that Harold returns south and there's either a stand-off ["remaining far from battle"] or a bloody period in which neither side won a clear victory?
To be honest I see the following problems:
a) Stamford Bridge [of the battle as opposed to the football ground
] is actually only a few miles from York so there's not really a lot of room for a defeated but living Harald to retreat to. Also with his army already in the north Harold Godwineson is unlikely to leave a continued threat there, possibly even after he hears about William landing.
b) Similarly, if Harold returns south at the same speed William is pretty much trapped on a peninsula and if he doesn't win a battle quickly will be straved out. Also Harold can continue to call on reserves from elsewhere to increase his forces so time is a crucial factor.
c) Neither Harold, a proud king and who's home estates are very near where the Normans landed, nor William, who has committed a lot to the invasion including offering a lot of English land to his mercanaries are likely to be willing or able to compromise.
d) While there are a lot of people of Viking descent in the north of England those are predominantly Danish in descent and if anything hate the Norse more than anyone else, especially since the two countries have been fighting for generations and Harald has been plundering Denmark for most of the last decade or so. As such I doubt a weakened Norse army would be able to maintain itself even if a victorious Harold didn't persue and destroy it.
As such I'm doubtful you could get the sort of partition your suggestion. There was something vaguely similar at the start of the century when England was partitioned between the English under Edmund Ironside and the Danes under Canute but that only lasted a few months and I can see a similar situation if somehow what you suggest developed. It might be more conplex with three main player but then Harald was more of a raider and pillager than a conqueror as shown by his actions in Denmark.
If somehow I did I doubt that you would see a partition based on that lasting until the present day. Any Norman lodgement in southern England, especially if ruled as savagely as OTL, would face the same problem as the Normans did OTL, but far worse. I,e, being torn between their British and continental interests, but with less resources. Similarly as I say the Norse would have difficulty retaining a prolonged presence in the north.
Therefore some interesting ideas but think they face serious problems to come into existance I'm afraid. I could see William still winning but in a different way, or Harold preserving English independence or even Harald possibly winning if William sails earlier and whoever wins at Hastings losing to the Norse but I doubt he would be able or possibly even willing to establish a lasting state in England.