Translation:That child is the black sheep of his family.
Το καημένο το παιδάκι...
I suggest "in his family" as well as "of..."
Is this expression actually used in Greek?
Yes, with the same meaning as "black sheep" in english.
Η ο μπαμπάς τα είχε με μαύρη προβατίνα....
I suggest "That child is the black sheep in his family" - grammatically correct and closer to the Greek.