Irritable woman and daughter join head, showing discernment (10)

'discernment' is the definition.
(thesaurus)

'irritable woman and daughter join head' is the wordplay.
'irritable woman' becomes 'shrew' (I am not sure about the 'irritable' bit.).
'and' means one lot of letters go next to another.
'daughter' becomes 'd' (genealogical abbreviation).
'join' says to put letters next to each other.
'head' becomes 'ness' (ness is a headland).
'shrew'+'d'+'ness'='SHREWDNESS'

'showing' is the link.

Can you help me to learn more?