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, so it 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!