If I may summarize and quote extensively from W. L Warren, Henry II? (Univ. of Calif. Press, the English Monarchs series, 7 volumes of which were offered as a bonus for a book club.)

"Henry's motives in going to Ireland are not easy to divine." The Irish bishops were victims of strong monastic power and had very much wanted English help -- King Murchetach O'Brien and others had not been capable of helping them and some bishops had travelled to Canterbury to be elevated. The pope similarly -- his legate's synod at Kells in 1152 had not accomplished much -- and had issued a bull of exhortation. At the time, Becket had just gotten his just deserts been killed, so some church approval might have come in handy, and Gervase of Canterbury wrote that Henry was going out of reach to stave off a possible interdict.

Dermot king of Leinster had come to Henry (in Aquitaine!) in 1167, 4 years back, for help but got only gifts and a letter of permission. Warren suggests that Henry was thinking of Ireland as like Scotland, where the sons of Malcolm Canmore had recruited Normans and taken back Scotland.

Dermot managed to recruit some help, but then scored Richard Strongbow fitz Gilbert de Clare, earl of Strigoil and son of the dispossed earl of Pembroke ... at the price of his daughter's hand and the inheritance of the kingdom. Henry's "reaction was to order Strongbow home, put an embargo on supplies to the adventurers, and punish anyone else who went to Ireland without his licence".

In 1171 Dermot died, and Richard got the kingdom and managed to rout Rory O'Connor, king of Connacht. "It was from just such small beginnings as these that the Norman kingdom of Sicily had risen to be a thorn in the side of the Holy Roman Empire and a powerful influence in the Mediterranean. ... But it was quite another matter to have prominent barons -- and a disgraced earl no less -- establishing a position of private power beyond his jurisdiction and control." I'll point out that English marcher barons, where they got land in Wales, were independent of the king and could build a power base (e.g., Chester) -- and I think the kings of France would have made some pungent comments on the problem of a vassal getting an independent kingdom on a nearby island.

Gervase wrote that both Richard and some Irish asked for intervention. The pope did: "'our dearest son in Christ'" to Henry, to the laity of Ireland enjoining obedience to "'that majestic king who is a devoted son of the Church'", this not long after Becket's obstinate roadblock on the path to a settlement was cleared death.

And as conquests went, Henry II's didn't. Ejecting the Normans would not have worked: Ireland had been advertised as a land of opportunity, and worse, the common notion was that any land a man could conquer was rightfully his. Richard de Clare surrendered his lands to hold it as a fief (minus ports and castles), but only some Irish rulers came in and proffered their fealty, and they did not hold their lands as fiefs. E.g., High King Rory O'Connor in the Treaty of Windsor of 1175 became the king of England's "man" but "he was to hold his land 'as fully and peacefully as he did before the lord king entered Ireland' ". He paid tribute and owed personal service, "but his authority as high-king was recognized over all of Ireland outside the territories of Henry and his barons".

Warren suggests that Henry was now thinking of Ireland as being like Wales, meaning after he gave up his inflexible demands for his grandfather's power and started to cooperate successfully with the major Welsh princes. "The Irish arrangement was a failure ... presumed too much upon the political maturity of Ireland ... the situation rapidly got out of control ..." Normans were recruited elsewhere. Henry had to divide up Munster into fiefs in 1177 to keep local Normans from "carv[ing] out private empires".

Warren suggests that Henry then thought of Ireland as being like Brittany. He had installed Prince Geoffrey as duke of Brittany, so he installed Prince "there's hope for every ape in Africa" John in Ireland, who promptly bungled it away. So everything failed.

And if it was a "conquest", it's in the running for Most Ineffectual Conquest in History, as firm royal control wasn't really started until Henry VIII and achieved until James I and VI, right? That was almost half a millennium later.

Can only really speak for Scotland as im currently studying it at uni. By the time Edward I was invited to help solve the dynastic crisis in Scotland he'd already conqurerd Wales and depending on how you interpret the sources (Treaty of Birgham is a good primary one just before the invasion) you could argue it was out of a wish to expand his power which he would have done had his son married Margret the maid of Norway but after her death he saw his oppertunity and took it for pure imperial ambitions (thats just my opinion and could be wrong). Hope this helps

Edward I went to Wales and Scotland for the sole purpose of conquest. He took control of Wales over the course to two military campaigns in 1277 and 1280, invading and colonising the country. He sought to meddle in the succession dispute in Scotland in 1286 and put a king on the throne, John of Balliol, but humiliated the man so much that eventually Scotland fought back, winning the Scottish wars of independence from 1296 to 1357. It was at this point that the Auld Alliance, between Scotland and France was formed.

Scotland would eventually join England when the King of Scotland, James VI, became King James I of England as well in 1603. After a century of personal union the two countries became one with the Act of Union in 1707.

Why? It is likely that Edward I simply wanted more land in places which were weak enough to be taken, but it is also likely that security was on his mind. With the entirety of the 'British Isles' under their control, the Kings of England were in a far better and more secure position in relation to the rest of Europe. The Auld alliance in particular meant that the English were never safe, even during the height of their power in the Hundred years war.

This fact became increasingly important in 1707, which the English parliament sought to choose their new king. The Scottish parliament had made it clear that they would choose who they wished, and this created the nightmare of a new Auld alliance, with French armies in Scotland bypassing the now powerful Royal Navy.