Is expiation obligatory for someone who swore an oath to resolve a problem between a husband and wife, knowing that he swore the oath without the intention of it being an oath?

The questioner did not clarify the reality of what she swore upon to determine its ruling. Swearing falsely is considered a yamin ghamus (a deeply sinful oath), which necessitates repentance and has no expiation according to the majority of scholars, though expiating it is more cautious. Ibn Qudamah says that one who swears falsely has no expiation because what he committed is greater.

It is permissible to swear falsely to save an oppressed person, and there is no sin or expiation in it, because expiation is for swearing concerning a future matter, not a past one. It is stated in Al-Fawakih Ad-Dawani that permissible lying occurs when saving a life or inviolable property from an oppressor, and there is no expiation for it in this case.