I also share similar understanding.
I think it means that after a woman gets married with a Greek man, though she may try very hard to understand the Greek culture, she still cannot fully incorporated in her husband's Greek family.
My understanding is that the family hopes a Greek woman to live with them, but the woman is probably not from Greece or she doesn't act like a Greek, etc...
My understanding is that the family hopes a Greek woman to live with them, but the woman is probably not from Greece or she doesn't act like a Greek, etc...