Ireland was split into many little princedoms and didn't meddle much in the affairs of other European countries, if at all. Quite early, however, the English kings became lords of Dublin and made the area around it the Pale of (English) settlement, and during the second half of the 14th century, quite a few English settled there. In 1400, the island of Ireland was hit by the Black Death, and relatively more English were killed, since they were concentrated in the cities. Generally, there was less English involvement in Ireland ITTL, since England was preoccupied with affairs on the continent, first because they stayed longer in Aquitaine, and second after they inherited Castille-Portugal.
In 1531, during the Great Occidental War, Prince Alasdair decided to extend the war to Ireland. He was successful in this too: 1533, Dublin was conquered by him. In the Peace of Barcelona 1547, the Quadruple Monarchy had to accept the independence of Scotland-Ireland under Alexander / Alasdair IV in Europe. The English would be expelled.
The sheer size of his empire meant that Alasdair hadn't much time to care for Ireland; despite this, or maybe because of it, the Irish were very content with his government.
Under English rule again
In 1606, king Henry V of Triple Monarchy of England-Castille-Portugal managed to become accepted as new king of Ireland, after the death of Alexander V. He was a capable ruler and didn't anger off the Irish; but under his son Henry VI, the Triple Monarchy fell apart again. During the first English Civil War, 1638, the uprisings in Ireland started, English were driven back into the Pale. In 1641, Dublin had to capitulate to the Irish, and many English fled to England or Markland.
After Humphrey I had won the civil war, he took a look on Ireland again. In 1662, England reconquered the Pale. The rest of the island stayed independent yet, which became important: In 1698, it was agreed that a new council would be held on neutral ground - in Ireland, since it was the only Catholic European country that had stayed out of the anti-French War. 1703, the council of Cork ended again with a compromise.
During 1718-23, Ireland was again completely conquered by Britain.