That lady had a divine responsibility for marriage and the family (4)
I believe the answer is:
hera
'divine responsibility for marriage and the family' is the definition.
I can't judge whether this definition defines the answer.
'that lady had a' is the wordplay.
'that lady' becomes 'her' ('her' refers to a woman).
'had' is a charade indicator (letters next to each other).
'her'+'a'='HERA'
Can you help me to learn more?
(Other definitions for hera that I've seen before include "Divinity" , "Greek equivalent of Juno" , "female Greek deity" , "Jealous sister and wife of Zeus" , "Greek goddess" .)