Very backward family with name right round Croatian port (9)
I believe the answer is:
dubrovnik
'croatian port' is the definition.
(I know that Dubrovnik is a croatian port)
'very backward family with name' is the wordplay.
'very' becomes 'rov' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'backward' is a reversal indicator.
'family' becomes 'kin' (synonyms).
'with' says to put letters next to each other.
'name' becomes 'dub' (as in dubbing someone with a particular name).
'kin' back-to-front is 'nik'.
'rov'+'nik'='rovnik'
'rovnik' after 'dub' is 'DUBROVNIK'.
'right round' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for dubrovnik that I've seen before include "Croatian port, once Ragusa" , "Croatian city, Ragusa to Italians" , "Croatian resort" .)