AHC/WI: the Ui Ímair/Ivar Dynasty unifies Britain and Ireland.

Greetings! First, I'm just a amateur when it comes to history, and I'm still learning about Scandinavian, british and Irish history. However, I thought this scenario could be interesting.

I already posted a similar thread a year ago (no one commented), but now I decided to post a slightly different, more plausible one.

Some context: the Ui Ímair were a norse-gael dynasty which claimed to originated from Ímar, the supposedly King of All foreigners (Norse) in Ireland, who is sometimes described as being the same as Ivar, the Boneless. They ruled over many territories in the British Isles during their existence, like Dublin, the scottish islands, Northumbria etc. Some compare them to the Rurikids, the difference being that they failed to create a comparable long-term legacy.

However, what if they did?

The challenge: have the UÍ Ímair be considered kings of Great Britain, Ireland and the other islands in the archipelago, from the years 1000-1200. It can be a heavily decentralized, or even somewhat symbolic title, but it can also be something more.

I have thought about preventing their expulsion from Dublin, or simply making them more successful at maintaining their conquests after it (they managed to reconquer Dublin and even take part of Northumbria and the Isle of Man after the event). However, I don't know which scenario would be more plausible.

What could be the cultural impact of a early unification of the archipelago by norse-gaels? Which language would have prevailed? How long could this small empire sustain itself?
Start with York. Have them be involved with the conquest of Wessex and tied to the victorious house of Guthrum and in doing so somehow end in the most powerful position, say ruling East Anglia and most of Mercia while Guthrum has a rebellious kingdom that takes years to put down.

That puts Ui Imair as rulers of most of England and Dublin. The York Anglo Saxons were becoming more Norse in custom and vice versa, so let the culture drift without any pesky House of Wessex (except perhaps one of Alfred's Guthrum raised daughters or granddaughters married in) to reinforce Saxon identity until the kings are the "natural" rulers and Anglo Dane culture is dominant.

Keep Dublin going. But in time, have these Anglo Danes reinforce Dublin and conquer Ireland, repeating the process. After that, it's done.