Yay, something I actually know a little bit about. I finished Lancaster and York: The Wars of the Roses by Alison Weir, just a couple weeks ago. The book covers the war and what preceded it from the death of Edward III, who created the duchies of York and Lancaster, through the death of Henry VI and Edward IV's consolidation of power. In the book, she makes little mention of Ireland except that a few times the major Lords over the area were sent to put down small and insignificant uprisings. Ireland did very little to affect the outcome of the war. Scotland, on the other hand, did play a role. After Edward IV took power from the Lancasters the first time, Margaret of Anjou, wife of Henry VI, ran to the Queen of Scotland, who gave her asylum in Edinburgh. Margaret, not Henry, was the primary force behind any Lancaster power as frankly Henry was an overly pious idiot who did not understand how to make policy or earn money for the crown, and it was from Edinburgh that Margaret was able to begin her pursuit of regaining the crown for her husband. From Scotland and northern England, Margaret was able to recruit a large army to retake the throne on the promise that she would allow her soldiers to ransack the south when London was retaken. She also negotiated for aid from the Scottish, including giving the Scottish the north English city of Berwick. While this trade secured aid for Margaret with the Scottish, it severely angered many Englishmen, as Berwick was a heavily contested city that many Englishmen had died to protect over the years. From Scotland, the Lancasters were then able to stage a campaign that removed the Yorks from power, though only for a few months. The Yorks, who were great at spreading propaganda and who had shown that they cared more for the English people than the Lancasters, were however quickly able to re-remove them due to the wide support of te commons. Later in the war, after the Lancasters had retaken and relost the crown, Margaret returned to Scotland in hopes of doing all this again, though this time she had fewer allies, both English and foreign, and so the Scottish were less willing to grant her much aid, though they did give her some supplies.

TL;DR: Margaret of Anjou ran to the Scottish nobility both times she lost power, and staged attacks against the Yorks with Scottish aid. The Irish played very little part at all in the war.