Is swearing an oath by divorce to boycott one's stepmother and not shake her hand considered a divorce for the wife? And what is the religious ruling on swearing an oath by divorce in matters unrelated to the couple's life?

The majority of scholars hold that swearing an oath of divorce is considered a contingent divorce. If the contingency occurs, the divorce takes place. This is contrary to Ibn Taymiyyah's view, who believes that its expiation is the expiation for an oath if one breaks it.

Accordingly, your wife has been divorced from you due to her shaking hands, based on the opinion of the majority, which is the stronger and more cautious view. However, she would not be divorced according to Ibn Taymiyyah's opinion, and you would be required to pay the expiation for an oath.

If the divorce has occurred, you can take her back before her waiting period (iddah) expires, provided it is the first or second divorce. The fact that the oath of divorce was on a matter unrelated to marriage is irrelevant; it falls under the category of contingent divorce according to the majority. It is important to note the impermissibility of this oath, as it involves swearing by other than Allah and exposing the marital bond to destruction.