Here is the item again:
Despite her parents' disapproval,
(A) Tran
continues to date Charlie.
(B) A nice young
man (C)
whose only fault is not being born Vietnamese.
You correctly realized that the period after Charlie created a fragment. A nice young man whose only fault ... is an appositive, which cannot stand alone as a complete sentence.
To fix this fragment, you chose to do this:
Despite her parents' disapproval, Tran
continues to date Charlie,
a nice young man whose only fault is not being born Vietnamese.
You have correctly applied Punctuation Rule 9:
Main Clause + , + Appositive.
Play that beautiful music!