This is a subject that is worth more than I can take up in John's valuable space. I will have to get a site of my own and try and explain the position.
Its a story of classic division where everyone is right but they end up at loggerheads with one another and cause a great deal of human misery.
Basically the extreme Presbyterians became convinced that their religion was the only true religion and tried to impose it first on Charles I who was equally convinced of his divine right to rule. Charles wished to rule through Bishops - this was totally repugnant to the Presbyterian camp. Charles, foolish boy, was trying to rule without his English parliament as he had fallen out with hem. he had money enough as long as did not have to fight a war.
The Scots had two uprisings against Charles which have gone down in history as the Bishop's Wars. The Scots basically won as Charles was initially not game to recall his parliament to raise money.
Eventally he succumbed and the parliament once in session made demands of him that eventually led to the Civil War and his eventual demise.
There was much too-ing and fro-ing over Scots support and the Whigs (the presbyterian party of the time) were in control and nothing would satisfy them other than a ruler who was subservient to the Church and the people. ie: a constitutional monarch.
These guys were ahead of their times and the times were not really ready for them.
Once Charles I was beheaded he Scots brought in his son as theri king Charles II. This was a red-rag to Cromwell who came up to Scotland and beat the Scots at Dunbar. (another story in itself).
The Scots were beaten but not defeated. It has been recognised that at the start of the civil war at least the Scots had the best army in Europe due to a tradition of serving as merceneries in various continental armies. Many of these returned to Scotland during these times to serve in the Scots armies as battle hardened veterens.
After Dunbar the Presbyterians formed an army in the South West as the Army of the Western Association. Another (the main army) gathered around Charles in the north. Charles II also believed in divine and absolute rule and had no time for the Presbyterians - he had many supporters of his views gathered with him. But he really needed the WA Army's help. Cromwell took Edinburgh and marched back and forth between there and Glasgow for some considerable time. He relised that the WA Army was soft in its support for Charles and tried mightily to woo them over to his side.
This caused a lot of problems for those of the WA as they wer first patriots defending their country from the invader Cromwell. However they wishes to extract a promise from Charles to support Presbyterianism and offered it to him on undiplomatic and humiliating terms. This Charles never forgave them.
Eventually the WA Army attacked Cromwell and were decisively beaten. The attack was probably rushed as it was generally known that Charles was in the process of replacing their generals. If they had merely retired to the southern hills and kept up a guerilla war the course of history might have been quite different.
In the end Charles rushed south with the northern army and was himself beaten and renderd a fugitive.
On his resoration to the throne he remembered the Presbyterians and their terms offered for support. He saw them as rebels and his sycophants saw an opportunity in fines and dispossessions as a way to restore their estates that had been lost. The attempt to re-impose Bishops and general heavy handed rule by the king's deputies in Scotland led to defiance, rebellion, covenanting and the forces of repression - executions, fines, dispossession, quartering of the Highland Host. this was the time when fines were imposed for "aiding Cromwell" and even for not turning up for church. It made the Presbyterian movement even more radical and many left for Northern Ireland in order to be able to pursue their religious beliefs with more tolerence. This might weem strange for the Presbyterians of that time were not famed for their own tolerence!
It only got worse with James II.
On the accession of William and Mary a more reasonable attitude prevailed and this was known in Scotland as the "glorious revolution". The Whig party again had the upper hand but the radicalisation calling for reform in government was far from done.

This is a brief overview from memory covering a very complex and confused period in Scottish History. I need to give it more justice in a condidered and researched article.
What I have tried to show is that there was a fundamental difference of opinion between the Presbyterian faction which believed that the king should be answerable to the people through parliament and to god through the church. the first part has become the principle of a good working constitutional monarchy. For the second I respectfully submit that they were a bit over the top.
On the other hand the later Stewart Kings had the evidence of the insecurity of the early Stewart Kings and once convinced of their divine right to rule were not about to give it up. A recipe for a clash of their various supporters. Parliamentary democracy was still decades, even centuries, away from being able to cope.
The covenanters of the South West were regarded as rebels and treated as such.
Consequently rash, radical, staunchly patriotic Presbyterians were persecuted in their own eyes even though they supported the institution of the monarchy.
Its a clear case of fault on both sides leading to a whole lot of misery where there should have been none.