Royals half-cut after cocktail somewhere in the Caribbean (10)

'the caribbean' is the definition.
Both the answer and definition are singular nouns.
Maybe you can see an association between them that I don't see?

'royals half-cut after cocktail somewhere' is the wordplay.
'royals' becomes 'queens' (queen is a kind of royal).
'half cut' indicates taking half.
'after' says to put letters next to each other.
'cocktail somewhere' becomes 'martini' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'queens' with half the letters taken is 'que'.
'que' after 'martini' is 'MARTINIQUE'.

'in' is the link.

Can you help me to learn more?