What is the ruling on the wife and divorce if the wife swore an oath by divorce that she would not inform her family of the problems between her and her husband, and then she informed them? And is it permissible to divorce her in absentia if the divorce occurs?

Scholars have differed concerning the ruling on swearing an oath by divorce and making it conditional. The fatwa adopted by us is that divorce occurs when the husband disobeys the command upon which he swore by divorce. Sheikh al-Islam Ibn Taymiyyah held the view that if swearing an oath by divorce is not intended to bring about divorce, then an expiation for an oath (kaffarat yamin) is required upon breaking it.

Accordingly, your brother's wife has been divorced from him due to her disobedience of his command. He can take her back during her 'iddah (waiting period) without requiring her presence or consent, and it is recommended to have witnesses for the reconciliation.