I don't know which schools you visited SB, but both my children attended a private school and they mixed very well with all the other pupils which consisted of a wide variety of nationalities including Cypriots!
I have never seen any evidence of 'looking down noses' or 'drugs' though I am not saying this does not happen as in this day and age, it probably will - in all schools, not just the privately run ones - children being children.
I suggest you/your wife/other family members etc all attempt to learn Greek and try if you can to converse only in Greek (not easy!), That way you will be helping your daughter and in turn educating yourselves.