What is the ruling on someone who swore an oath of divorce, intending his mother, not his wife, [saying] "By divorce, I will not go out with you on any trip"? Is he bound by an expiation along with a reprimand, as happened to him the first time?

An oath sworn by divorce has the same ruling as a conditional divorce. If the sworn-upon condition is met in the manner intended by the one who swore the oath, then he has broken his oath, and divorce occurs, according to the majority of jurists, even if he did not intend divorce.

So, if you went out with your mother and your wife, the divorce occurs according to what is fatwa-ed by us, which is the view of the majority. If you only intended your mother, then the divorce occurs by your going out with her, not with your wife. If the motive for this oath, as you mentioned, was your mother's illness, then if she recovers and you go out with her, you would not have broken your oath.

One must be cautious about swearing oaths by divorce, especially doing so frequently.