You don't use the definite case if the possessive is before the noun, so the latter would be "Vi liker din ku".
'ku' is a feminine noun, meaning it can be inflected as both 'kua' and 'kuen'. If you're using the feminine inflection, you ought to use the feminine possessive 'di'.
Either of these work:
While mixing these, like "di kua" or "kuen di", doesn't work.