http://www.clanmacalistersociety.org/historians-corner/article1.htm
This clan was from the SW corner of Scotland (Ayr) and sailed amongst the islands mentioned previously. The distance from the Scottish Isles to Northern Ireland is less than 20 miles, so intermarriage would certainly happen.
According to the history above, the King of Norway controlled these islands up to the 12th Century.
I'm proud to be from a smaller Clan within the Macalisters...:^)
I saw a book a few years ago that was about using DNA to trace relationships, and it had a chapter on the descendants of Somerled--the current leaders of the clans let their DNA be tested and they all had the same Y chromosome (in other words, in their direct paternal lines, there was never a female ancestor who had a son by a lover instead of by her husband).
Back in the 1970s a professor in Edinburgh named Sellar had an article on Somerled where he argued that he was of Gaelic ancestry, but the DNA evidence seems to prove that he was Norse.
There are surviving documents with Alexander of Islay's seal on them when he submitted to Edward I in the 1290s (I've seen them in the Public Record Office in London). That seems to have more to do with the fact that family rivals were supporting Balliol than any love of Edward I.