Rather between a conservative monarchy that wanted to support the Germans but was not in a position to do so and a liberal prime minister whose prime constituency was the middle classes/diaspora Greeks. Securing the survival and well being of Ottoman Greeks was not just a matter of policy it was the vested interest of the very political forces that supported the Greek liberals. From the point the Young Turks start ethnic cleansing them in 1914 options varied from a minimum of saving their lives and as much of their capital as possible hence the negotiations for an exchange of populations in mid 1914 to the maximum of Greek control of the Aegean coast of Asia Minor, after the Ottomans most conveniently entered WW1 putting their collapse into the cards.I admit I'm not entirely sure about Greek history but at the time their was a major clash between a conservative monarchy who wished for neutrality in the war as Grace was still a pretty young nation and felt it would have lost to much to to join either way and focus on digesting the ground it gained in the Balkan war (Greece doubled twice in size) and a jingoistic prime minister who wanted to support the British and attack Bulgaria and the Ottomans.
If there was a coup it was very clearly on the Royalist side when Constantine first dismissed the elected government, then after fresh elections in May 1915 delayed for several months the formation of a new government by the elected majority and then overthrew for a second time the elected government, that had won a massive majority just a few months before. Nevermind conspiring with Bulgarians, Germans and Austrians behind the back of his own government and after 1916 letting the Bulgarians occupy Greek territory (with none too good effects on the inhabitants).Obviously neutrality was increasingly comprised over time and basically a coup and Entente basically occupied large part of Greece till it got a government suited for their purposes.