Hard time coming back down south to Reading and Maidenhead in a cloudburst (12)

'a cloudburst' is the definition.
(a cloudburst is a sudden rainstorm)

'hard time coming back down south to reading and maidenhead' is the wordplay.
I cannot quite understand how this works, but
'hard' could be 'h' (abbreviation used in pencil classifications) and 'h' is present in the answer.
'time' could be 't' (abbreviation) and 't' is present in the answer.
'down' could be 'under' (under means further down) and 'under' is found in the answer.
'south' could be 's' (abbreviation) and 's' is found in the answer.
'to' is present in the answer.
'reading' could be 'r' (one of the traditional three R's of education) and 'r' is located in the answer.
'maidenhead' could be 'm' (head letter of 'maiden') and 'm' is present in the answer.
This accounts for all the letters.
This explanation may well be incorrect...

'in' is the link.

Can you help me to learn more?