Two daughters interrupting irritating type, who poses a problem (7)
I believe the answer is:
riddler
'who poses a problem' is the definition.
(a riddler poses riddles)
'two daughters interrupting irritating type' is the wordplay.
'two daughters' can mean two replacements for 'daughters'.
'daughters' becomes 'd' (genealogical abbreviation for daughters).
'daughters' becomes 'd' (genealogical abbreviation for daughters).
'interrupting' is an insertion indicator.
'irritating type' becomes 'riler' (someone who riles people up).
'd'+'d'='dd'
'dd' inserted within 'riler' is 'RIDDLER'.
(Other definitions for riddler that I've seen before include "passing on only the finest material?" , "Sphinx?" , "Puzzle setter" , "Deviser of ingenious questions" , "setter of puzzles" .)