
Aight, please excuse any rookie mistakes in the scenario I'm laying out below - this is well outside my historical "comfort zone" (West and NW Africa) and I'm mostly working off one source:
After King Magnus Barelegs died in Ireland in 1103 CE, there was a protracted battle for inheritance between the surviving sons of Godred Crovan. Eventually Olaf the Red, Godred’s youngest son, won this First Manx Civil War, and he reigned for 40 years, before being slain by his nephews. Olaf was succeeded by his son, Godred II (the Black), who was also invited to be King of Dublin.
Unfortunately, Godred II spent too much time concentrating on his Irish holdings, and he lost the Kingdom of Man and the Isles in 1158 to his brother-in-law, that canny warrior and politician Somerled, Thane of Argyll. Somerled (whose name apparently translates from Norse as “Summer Sailor” which is awesome and who was described as “a well-tempered man, in body shapely, of a fair piercing eye, of middle stature, and of quick discernment” in the Chronicle of Mann) reigned for 5 years, before being killed at Renfrew while fighting a battle against King Malcolm V of Scotland. His kingdom then fell apart, having not been prepared to lose their warrior-king yet with Somerled having left the issue of succession for later times.
So, to keep the maritime kingdom of the Summer Sailor together, I propose changing not the famous Battle of Renfrew, but the considerably more minor Battle of Epiphany. Even if the political center of the Norse-Gael Crovan dynasty had shifted to Dublin, in many ways, the Isle of Man remained the heartland of the kingdom and was the main recruiting source for the King's troops. Throughout his campaigns, Somerled was forced to rely on Irish clan warriors to bolster his forces, many of whom were unreliable and ineffective against the gallowglass-like Norse-Gael warriors that Somerled preferred to use. The constant need to protect his half of the Isle also regularly drained him of available soldiers. If Epiphany results in a victory in the "Half-War" that allows Somerled claim the whole of the Manx heartland instead of just around half, could he turn this around into a lasting dominant presence in the Irish Sea? Would Somerled's descendants rule as clients of Norway, as the Crovans did after Magnus Barelegs' punitive expedition? Would they perhaps turn to England as Rǫgnvaldr did later?