Ah, could this mean that England and scotland could be unified up to 500 years earlier?
also would Norse Ireland be a vassal?
My inspiration is Magnus Barelegs here. In 1098, so thirty years after your POD, he was king of Norway and he came to the british isles so secure his rule over the norse there.
In that campaign, he took control of the isle of man, the welsh island of Anglesey, the Scottish isles of the Hebrides, Orkneys and Shetlands, parts of mainland Scotland around the very north and very west and Dublin and the surrounding area in Ireland.
And he did that without having to fight any of the major british kings. That area was most occupied by norse speakers and was not under the influence of either Scotland or England.
Now 30 years earlier I think things are slightly worse for the Norse, they've been kicked out of Ireland in 1064 by the man who in otl teamed up with Harolds sons to invade England. And the norse irish sea kingdom has been reduced to just Galloway.
But if, once Harrada has pacified England he wants to lead a second british campaign, then the irish sea and that preexisiting norse empire seems a more likely target than wales.
Again the main point in replacing William with Harald is to see how the latter behaves differently. In OTL William campaigned in Wales, I can see Harald going for Dublin instead.