Pigeon in port briefly with stick from Brighton? (4,4)

'pigeon' is the definition.
(I know that rock dove is a type of pigeon)

'port briefly with stick from brighton?' is the wordplay.
'port' becomes 'dover' (port town in Kent).
'briefly' means to remove the last letter.
'with' says to put letters next to each other.
'stick from brighton?' becomes 'rock' (I can't explain this - if you can you should believe this answer much more).
'dover' with its last letter removed is 'dove'.
'dove' put after 'rock' is 'ROCK DOVE'.

'in' is the link.

Can you help me to learn more?