Relative's American in the money (6)
I believe the answer is:
cousin
'relative's' is the definition.
(cousin is a kind of relative)
'american in the money' is the wordplay.
'american' becomes 'US' (United States).
'in the' indicates putting letters inside.
'money' becomes 'coin' (coin is a type of money).
'us' placed into 'coin' is 'COUSIN'.
(Other definitions for cousin that I've seen before include "An aunt's or uncle's child" , "Kinsman, generally (archaic)" , "Address used among sovereigns" , "Relation, could be kissing" , "Aunt/uncle's child" .)