"Is my son well behaved?"
Translation:A bheil mo mhac modhail?
Of course they’re not interchangeable – the former means my son and the latter my daughter.
As for difference between the construction – mo mhac is more regular, as the possessive pronouns (mo, do, a, etc.) are used for inalienable possession – things that are naturally yours: body parts, family members, etc.; while the construction an X aig Y for Y’s X (like an taigh agam my house) generally is for things possessed alienably – ones that you can buy, sell, give away, lose by leaving somewhere and forgetting where, etc.
But there are exceptions, and one of those is that my husband is always an duine agam (and not *mo dhuine) and my daughter is typically an nighean agam (and not *mo nighean; although dictionaries do mention a nighean as her/his daughter in some expressions).
Acc. to Akerbeltz, mo nighean could be understood as my girlfriend rather than my daughter.
See Possessives and syllabic structure or Ar n-Athair a tha air nèamh on the Akerbeltz wiki, which lists some nouns that typically go with possessive pronouns and ones that typically go with an + aig.