What is the ruling on swearing by "By God, it is as if my family is not in the house" while I know they are present, and does this entail expiation, knowing that I did not assert that?

This oath of yours is from the category of a 'vain oath' (laghw al-yameen), which is uttered unintentionally and for which there is no accountability, as Allah says: "Allah will not impose blame upon you for what is unintentional in your oaths, but He will impose blame upon you for what your hearts have earned." And it is incumbent upon a Muslim to seek truthfulness and avoid falsehood, as the Prophet (peace be upon him) said: "Beware of lying, for lying leads to immorality, and immorality leads to the Hellfire." If one needs to avoid stating the full truth, they can resort to dissimulation (tawriya) and ambiguous speech.