I've always been taught that the reason why Ireland had the troubles is ultimately due the English invading, dividing up the land, and then ruling feudal systems from London. Is this the true story?

I'll address this first, in the most detail, as it is closer to my area of expertise than Scotland, but I'll address Scotland at the end.

I will try to keep this as succinct as possible:

Ireland's 'invasion' starts with an abduction: Diarmait Mac Murchada, King of Leinster, abducted the wife of another king. This was an exceptionally bad political move on Mac Murchada's part: he already had a tenuous hold on his kingdom and his attempts to retain it had already alienated him from other kings, meaning he had no allies that could defend him in this situation, and you kinda want some good allies if you're stealing another king's wife.

Mac Murchada appealed to Henry II, for a lack of anyone else. Henry II was personally involved and landed in Ireland in 1171. During his trip to Britain, Mac Murchada secured other allies and with their assistance, captured Wexford. After this success, as their numbers were larger (reportedly about 3000) then marched on Osraige. The defeat of Osraige alerted another king, Ruaidrí Ua Conchobair, who created an alliance of the entire island of Ireland against Mac Murchada. As I am trying as hard as I can to keep this brief, eventually Ua Conchobair submitted to Henry II, giving him 'Lordship' over Ireland - as Ua Conchobair was recognised as the 'High-King' of Ireland.

Important to understand here, is that Irish kingship is not the same as English kingship. Irish kingship had a variety of levels and Irish kings were constantly at war with each other, claiming and losing lands. There was no single 'king' of Ireland, and really, every king had an equal claim to the title of 'high-king,' because frankly, no one was really high-king in any tangible sense.

However, this is misunderstood mainly by Giraldus Cambrensis (Gerald of Wales.) His Expugnatio Hibernica is a primary source account of all of these events and he understands Ua Conchobair's submission to Henry II as the entire island being given to Henry II (to be fair, it may be a willful misunderstanding as Giraldus is the president of the Henry II fanclub.) Ua Conchobair more than likely saw his submission to Henry as no big deal, as submission was a common practice among the Irish kings.

Now, also important is Laudabiliter: in 1155 Pope Adrian IV gives papal recognition of Henry II's dominion over Ireland, meaning, Henry II was king of Ireland. Historians have been calling its legitimacy into question for a long time, and you'll find arguments on both sides. I'm not fully sure where I stand on the issue but I do find it odd that Henry II never invoked Laudabiliter. Before Ua Conchobair's submission, he could have easily asserted his dominance over Ireland and chose not to. Anyways, tangent of my personal interest aside, here's where we are now: Henry II is Lord of Ireland because of the 'High-King's' submission to him, and he also has a papal bull stating that he can be king.

After the Norman invasion, things are (relatively) calm. Plenty of Britons move into Ireland and integrate fully into the local culture, by marrying into Irish noble families, and forming an aristocracy. The imposed English-style legal codes, parliament and administration really only affected this upper-class and did not serve the 'regular' folk. The Statutes of Kilkenny (1366) shows that the English were concerned about just how well the English were integrated as it imposes a variety of laws on how the English are to behave: discussing the unfavourable Irish customs that they have adopted and offering more palatable English customs as the 'correct' ones.

Henry VII, Mary I and Elizabeth I all sent military expeditions to try and Anglicise the Anglo-Normans who, at this time, were still considered too Irish. Not only were the Anglo-Normans expected to relinquish Irish culture, but the native Gaelic chieftains were ordered to relinquish their culture as well, and live as English nobles in order to retain their lands. After Ulster was devastated by English forces, the Gaelic lords took part in 'The Flights of the Earls:' an exodus from Ireland. This allowed the English crown to confiscate their lands and redistribute them to Protestant English lords, in what is known as the Ulster Plantation, resulting in a small number of foreign elites holding the majority of the land.

By the nineteenth century, the peasantry of Ireland were, to a large extent, reliant on a land-owning class that was usually (though not always) Protestant and, despite having inhabited Ireland for centuries, still culturally English.

This sets the stage for the 'turbulence' that you're certainly thinking of, though Ireland's history is far more complicated than I have briefly explained. You can easily imagine though, how tensions would arise in this situation: you have a working-class people who are of a different culture and religion than their landlords, who also feel a certain affinity to their home as their family has lived there for centuries. Some landlords were absent, yes, as per your question, but there were plenty who did live in Ireland. You have a divide, of class, culture, and religion -and language, until the decline of Irish after the famine- with the foreign group (largely) being on the 'winning' side.

As for Scotland, firstly, as a disclaimer, Scotland is not my area of expertise and I welcome anyone better versed in Scottish history to please answer OP's question better than I possibly can.

Secondly, Scotland wasn't 'invaded' by the English, at least not in the same way. The Wars for Scottish Independence in the 13th and 14th centuries did begin with an English invasion, but they were largely unsuccessful as Scotland remained independent. Ultimately, Scotland's union with England began in 1603 when James VI of Scotland became James I of England. While they remained separate political entities (and the idea of a union was widely opposed,) James viewed Great Britain as united as one realm.

A century later, in 1707, there was the Act of Union, which officially united the two nations. It was unpopular, and there were riots, but there weren't (as far as I'm aware) any serious revolts. So I suppose, why was there less turbulence in uprising in Scotland? Probably because their union with England was more political than martial: Ireland had been subjected to centuries of plantations and invasions, whereas Scotland was ultimately united with England through politics.

Some sources:

A New History of Ireland volume III, especially the first five chapters are excellent.

Giraldus Cambrensis' Expugnatio Hibernica

Fleming, Deborah "A man who does not exists" The Irish Peasant in the Work of W.B. Yeats and J.M Synge 1995

Frame, Robin, Ireland and Britain 117-1450 1998

Keating, Geoffrey, The History of Ireland translated John O'Mahony, 1857

Lockyer, R. James VI and I 1998

Mullally, Evelyn The Deeds of the Normans in Ireland. La Geste des Engelsi en Yrlande. 2002

Orpen, Goddard Henry Ireland Under the Normans 2005.

Whatley, C. The Scots and the Union 2006

(1) Scotland won, in the end. The English claimed dominion over Scotland, but were unable to hold it, and eventually recognized Scottish independence. This meant that (2)

(2) Scotland had its own kings and lords in place. Whatever feudal system existed in Scotland, the power in it was held by native Scots. (Ish. It's complicated. Many of them were descendants of Norman knights or Vikings.)

(3) In 1603, the Queen of England died, and her nearest relative was...the King of Scotland. Who became King of England also (James the VI and I). Two independent countries, but one ruler. Who had no need to conquer a country he already ruled.

(4) This was different from Ireland, where after defeat in the battle of Kinsale in 1603, a significant chunk of the native aristocracy in the northern part of Ireland (Ulster) fled to Spain. They were never able to regain power, and instead England was able to hand their lands over to English and Irish lords loyal to England. And

(5) England also imported peasant farmers to occupy these lands and solidify their hold on them. Specifically, they imported Protestant peasants. (The Plantation of Ulster). The English monarchs were Protestant, their greatest enemies/rivals were the Catholic monarchies of Spain and France. Part of the reason England really started trying to exert much tighter control over Ireland in the 16th and 17th centuries was because they feared that Catholic Ireland could be use as a base to invade them.

(6) Scotland was already majority-Protestant by the mid-17th century. Many of the peasant settlers who took part in the Plantation were Scottish. Their descendants are known as the Scots-Irish or Ulster Scots (a bunch of 'em later emigrated to Appalachia in the US and started country music).