Does swearing falsely to appease one's wife—with the intention of not being held accountable—necessitate sin and expiation?

A wife does not have the right to make her husband swear oaths regarding private matters. It is permissible for the husband to appease her and use equivocation in his oath, intending something other than what the wife understands. For instance, he might swear that he did not give his mother money, intending a specific time. If the husband swears and intends something else, there is no violation of the oath and no expiation due.

However, if he swore not to assist his mother financially and did not intend anything else, and then he did assist her, he must offer expiation for breaking an oath. His intention that his oath was a "laghw al-yameen" (idle oath) does not prevent the violation and expiation, because it is not an idle oath. There is no sin upon the husband whether he fulfills his oath or breaks it, because helping one's mother is a righteous deed.