"My father is grumpy."
Translation:Tha m' athair greannach.
Take a look at the article Possessives and syllabic structure or Ar n-Athair a tha air nèamh on the Akerbeltz wiki – it explains nicely the an X agam vs possessive pronouns (mo X, etc.) difference.
In general you’re right you’d use possessive pronouns with family members: m’ athair my father, mo mhac my son, mo bhean my wife, etc.; but there are exceptions, and this is one of them, according to Akerbeltz, mo nighean could rather mean my girlfriend than my daughter… (Similarly my husband is always an duine agam and never
On the other hand, the Dwelly’s dictionary gives mo nighean as my daughter in the entry for mo, so it is possible at least in older language – but the default in this case, anyway, would be an nighean agam.