The simple answer is that native Wales was conquered by Edward I in 1282. While the process had been a long and incremental one, with numerous setbacks for the English, the death of Llywelyn the Last and the subsequent failure of successive rebellions meant that Wales had finally been subsumed into the Kingdom of England.

Edward I was aware of the magnitude of the situation and did quite a lot to fully assimilate the newly conquered territory. He encouraged English settlers to immigrate into the newly set up towns and urban areas, as well as giving certain lands to his nobles. The Earl of Lincoln, for example, was given the lands surrounding Denbigh, and proceeded to import English families to work the lands - in many cases pushing native Welsh off the land in the process.

Edward also set up a new system of laws and governance that mostly did away with previous Welsh laws - Edward truly felt that many Welsh traditions were outdated, especially when it came to criminal law. In most cases civil and inheritance laws were allowed to survive, but almost all criminal laws were replaced with English examples. Some of this can be found in Edward's Statute of Wales, passed after his major victory in 1282-83

In addition, as mentioned before, the process of conquering Wales had been very gradual and this meant that English, Norman and even Flemish populations had been encroaching and intermixing with the Welsh populations for quite a while. More than half of what we today call Wales was under Anglo-Norman dominance by the time of Llywelyn's final defeat in 1282-3. This meant that the "better connection" you mention in your question had been being formed for quite a while, and in a far more complete manner than in Ireland or Scotland.

All this is in contrast to Ireland and Scotland. Scotland of course remained a (relatively) independent nation up until the act of Union in the early 18th century, over 500 years after the events we are discussing. While there were numerous attempts by the English, especially during the late 13th and 14th centuries, to establish dominance over Scotland, they more or less failed in the end. Figures like the Bruces, Balliols and Stewarts vascillated between subservience to England and independence, but in the end the Independence mindset won out. Despite major military defeats (Falkirk, Dupplin Moor and Neville's Cross to name a few) the Scots hung on during the wars with England, often resorting to guerilla tactics and avoiding battle. In any case, while the nobility of Scotland was in many ways descended from the same stock of adventurers who had taken England, by the 14th century they had a very different outlook and wished to remain independent. What's more, the laws, traditions and histories of the two kingdoms were very different. This is all a long winded way of explaining why Scotland remained more separated from England during this time.

Ireland is a more complex situation that I am not quite as familiar with, but I will attempt to give a good overview. The reason Ireland becomes a bit muddy is because in some ways there was more English domination and conquest in Ireland than in Scotland. After Henry II named his son John lord of Ireland, the entire island was supposedly under the jurisdiction of the King of England. However after John many English Kings refused to visit, instead focusing on their English, Welsh and continental possessions. As a result there remained a strange balance between Anglo-Norman families who had emigrated since 1169 and the Irish Kings, who in many ways asserted their independence. There was a low-level constant war between the two groups, occaisonally interrupted by greater conflicts or the attention of various English Kings. In general the English King actually didn't want his nobles expanding too rapidly - this could represent a challenge to his authority in an area that was hard to reach. In any case the King often saw the smaller Irish kings as his subjects, and at times supported their agendas against his English subjects.

However there also remains the question of demographic assimilation. Just like in Wales, the English were eager to import lower-class citizens into the newly conquered areas of Ireland, and many did come. Because its nearly impossible to keep two groups from intermingling, there grew up a large mixed population in Ireland that had equally mixed loyalties and identities. While this in some ways resembles the situation in Wales, the process was far more blurry in Ireland. Regardless, the process of total domination took a far longer time in Ireland than it did in Wales, and from the modern outlook we can see that Irish identity and independence remained a strong force into the present day. Not that the Welsh did not, but it had been more thoroughly quashed in Wales than Ireland during the late 13th and 14th centuries.

For reading on this particular subject there are some great works out there. I would recommend Domination and Conquest by R. R. Davies. Also, Davies' work The Age of Conquest: Wales 1063-1415 gives a more in depth look at Wales during the time period you are asking about. For a look at Scotland during this time, I would recommend Michael Brown's The Wars of Scotland, 1214-1371 as well as David Oram's Domination and Lordship: Scotland, 1070-1230

Hope that was helpful!