As I remember, all the way back to National School, the standard narrative for why Ireland was never a fully consensual part of the English, later British, state was because Ireland stayed resolutely Catholic at a time when England broke with Rome and decided on a path of Protestantism, albeit a very watered down variant.
But why did Ireland stay with the Church of Rome when the Crown in England decided to break with European unity and go its own way? An event with such resonance today that Henry VIII has re-emerged as a role model and icon for today's Brexiteers.
In 15th century Ireland there were effectively two nations: the Hiberno-Normans, loyal to the Crown and descended mainly from adventurers who had come over in the 12th century and grabbed significant landed estates for themselves, and the Gaelic Irish, who had originally been subdued but who had undergone something of a resurgence in the centuries since the Norman conquest. Of course there was a significant hybrid nation as well with much cross-pollenation of each society, a process which led many of the Normans to be described as "Hiberniores Hibernis ipsis" or "more Irish than the Irish themselves".
Many descendants of earlier Norman invaders had by the 15th century, intermarried with Gaelic aristocrats, become Gaelic speaking, dressed like the Irish (who didn't wear pants, much to the disgust of notable medieval chroniclers such as Froissart) and had followed many Gaelic cultural norms such as fostering of sons, patronising of Irish bards and musicians, land ownership and use etc.
Despite attempts in the 14th century to impose rigid English cultural orthodoxy on loyal subjects (The Statutes of Kilkenny) the Gaelicisation of Ireland had continued apace.
The Hiberno Normans did, however, retain strong ties in England with ongoing marriage alliances with their "compatriots" and loyalty to the throne albeit at an arm's length with much of the governance of Ireland entrusted to established Norman families, especially the Fitzgeralds.
An example of a noble English family with strong Irish connections was that of Lionel Plantagenet, Duke of Clarence and second son of King Edward III. He it was who had convened that parliament in Kilkenny to try to compel, among other things, loyal English subjects to keep their hands off Irish women (yeah. That worked out well!). Clarence's first wife had been Elizabeth de Burgh, the Irish born Countess of Ulster who had presented him with a significant parcel of Irish land as a dowry.
The Wars of the Roses which erupted in the mid 15th century were essentially a dynastic dispute as to which of the sons of Edward III provided the true line of succession to the English throne. Although they were all long dead by then, there had been all manner of usurpations and regencies in the century or so since Edward III's death. His eldest son, the Black Prince, had predeceased him and that man's son, Edward's grandson Richard II, had been deposed by Henry IV, the son of Edward's third son, John of Gaunt.
When Henry IV's effete infant grandson Henry VI ascended the throne 35 years later, the descendants of Edward III's second son, the aforementioned Lionel, Duke of Clarence, insisted that they were the rightful heirs. In simple terms, these were the House of York (white rose) and their opponents were the House of Lancaster (Red Rose). They fought a bloody series of campaigns over 20-30 years, culminating in the defeat of the Yorkists, led by then by Richard III at the Battle of Bosworth and the ascension of Henry VII to the throne.
The Norman Irish, perhaps due to the strong Irish connections of Clarence, by and large supported the Yorkist claim. During Henry VII's reign, there were at least two attempts to replace him on the throne with young men who claimed to be descendants of legitimate Yorkist claimants. Although both of these men (Lambert Simnel and Perkin Warbeck) were almost certainly imposters, they received strong backing from Hiberno Norman nobles, to such an extent that Simnel had even been crowned as Edward VI in Dublin, with significant Irish support.
Not suprisingly, the Lancastrian Kings decided that Ireland had to be brought closer into line to prevent future threats to the reigning Tudor (as the Lancastrians now called themselves) dynasty. Poyning's Law in the 1490s made the Irish (effectively Hiberno Norman) parliament subservient to England's and much closer scrutiny was made of the hitherto largely independent Fitzgeralds.
When Henry VIII broke with Rome in the 1530s he met with major resistance in England. As a large part of his reason for assuming "Supremacy" over the Church in England was to marry a fecund young woman who could produce a son or sons who could safeguard his dynasty and prevent a Yorkist resurgence, it is not surprising that much of the Catholic resistance to his reformation came from those loyal to the Yorkist cause. Yorkshire remained stubbornly "recusant" for a long time.
The Irish Norman Lords also tended to be reluctant to support Henry's break with Rome. Probably because of their enduring Yorkist sympathies?
It was round about then that a general coalition between previous enemies the Gaelic Irish and the Norman aristocracy began to emerge in hostility to the crown or at least hostility to its "reformed" members. The Old English and the Gaelic Irish became allies in the fight against Protestant "planters" brought over to try to tip the popular balance in favour of Protestantism, notably in Laois-Offaly, Munster and finally and most effectively in Ulster.
Would the fate of Anglo-Irish relations have been different if it were not for the Wars of the Roses and the British Irish of the day (the Hiberno Normans) backing the wrong horse?