The short answer is no, the Vikings who settled in Ireland, commonly known as the Hiberno-Norse, were not any more or less violent/warlike/peaceful than those Vikings who settled elsewhere in Europe. In fact, they fit pretty well into the pattern of Norse settlement outside of Scandinavia in the Viking age, which was one of close and (relatively) rapid integration into the political landscape of the settled region. (In making this statement, I'm excluding Iceland, Greenland and all other North Atlantic settlements; they were qualitatively different due to being virgin soil at the time of settlement.)

The Normandy example you give is, unfortunately, a bit of a red herring. Viking settlement in Normandy was limited, and took place after the grant of Normandy to Rollo by King Charles the Simple in 911. Within a generation, the Normans had been fully integrated into Frankish politics, culture and had been Christianized. (An easy example of this is the name given to his son by Rollo: William - significantly not a Norse name but a Frankish one). By the 1040s, when Normans begin their conquests in Southern Italy, or 1066 when they conquer England, the Normans are, for all intents and purposes, French, with no tangible connection to Scandinavia except for the cultural distinction of nordmannitas, the creation and performance of which is a whole different question. I'm not aware of any more conquests in the Basque country.

As for Dublin, and other Viking settlements, once again we begin to see that within about a generation of their foundation (c.850) they are well integrated into Irish politics and the politics of the Irish sea region. They begin to marry into Irish dynasties, give their children Irish names and by the early 900s we have evidence of a prominent Dublin dynasty, the sons or family of Ivar, whose entire political world is in the British Isles, with no political ties to Scandinavia. One innovation the Vikings seem to have brought to Dublin was to be more ambitious in their dominance of the Irish sea region, and the kings of Dublin were also kings of Man, the Western Isle of Scotland, York and possibly Galloway during the tenth century. They also held onto their identity as 'foreigners' (gall in Irish), much as the Normans did in France, right up to the English conquest in 1169. Dublin maintained strong trade links with Scandinavia, Old Norse seems to have been a commonly spoken language and the city even had a pagan symbol of authority, the pretty mysterious 'ring of Thor'. Right into the 12th century, the ruler of Dublin was known as rí/tiarna Gall (King/Lord of the Foreigners) by Irish chroniclers.

But despite these cultural differences, from the 960s onwards Dublin, and other Viking settlements like Limerick and Waterford, were pretty much integrated into the political landscape and when they fought it was in the context of Irish politics, like at Clontarf in 1014. They were hugely important in Irish politics, however, due to their populations, navies and wealth, and were fought over fiercely by rival Irish claimants to the High Kingship from the 10th to the 12th centuries. In a landscape dominated by these great families, Dublin was really the only city to continue some sort of independent role, primarily because it was the largest and most powerful. Its importance also meant that for much of the post-1014 period, the title of King of Dublin (rí Gall) was given to the son/heir of the most powerful king in Ireland, since controlling Dublin (i.e. it's wealth and military forces) was vital to successfully upholding a claim to the High-Kingship.

TL;DR: Dublin was no more or less peaceful than other areas of Viking settlement, but was pretty quickly integrated into Irish and Irish Sea politics, which was where its military energies were spent.

I wonder if the Battle of Clontarf had anything to do with this. Although, it did not occur until 1014. Anyone have more info on this?