First of all we must said something. In Greece at the 60's there were many powers that fighted one another. Everyone importand enough had an agenda and the good of the Country wasn't necesary number 1 priority
what I mean:
Frederica wanted to keep the monarchy influentional enough into the political life
Karamanlis wanted to be indipendant and make his own course ( he was a very ambitious man).
Andreas Papandreou ( another ambitious one) wanted to become a dominal figure into the public life even though if he had to stand up against his father
Papandreou the Elder wanted to create a strong , unified central party with mild opinions, become he hoped that the Kennedy administration would trust him as much as the right parties.
American officers in Greece wanted to make sure that whoever was ruling the country would behave in a way that it would keep up with the USA's policies concerning the Eastern Mediterranean.
Mess , isn't it?
when it comes to Karamanlis and the monarchy , there was a complex relationship. Karamanlis I tend to believe was chosen as a leader for the right, by the amaricans, the right politicians AND the palace because he was a fresh, scandal free figure. After a while of course he wanted to stop being a "pawn" and tried to have his own course.Thinking he was powerful, he stubbornly in many cases collided with the palace. This was intorelable by all those who had chose him , so he was forced to leave embitterd to Paris after resigning.
ps Years after he had his revenge when he played a crucial role in the aboliton of the monarchy. Once again in his agenda
there was no number 1" make sure the Greeks stop suffering from the political tension." the was number 1 " make sure to have Frederica and the whole dynasty destroyed" It was a payback