Does divorce occur with the statement, "Upon me be divorce, I have no business with you, and I will not interfere in your affairs after this day," if the wife is absent?

The presence or knowledge of the wife is not a condition for divorce to take effect. The fatwa adopted by us is that divorce occurs upon breaking an oath, whether the husband intended to enact divorce or merely to threaten. However, some scholars, like Ibn Taymiyyah, hold the view that an oath not intended to enact divorce has the ruling of an oath by Allah, and thus requires an expiation for an oath.

Therefore, if you interfered in your brother's matter, your divorce has occurred. You may take your wife back before the expiry of her 'iddah, as long as this divorce does not complete the three divorces. However, according to the view of Shaykh al-Islam Ibn Taymiyyah, if you swore with the intention of threatening and did not intend to enact divorce, then divorce has not occurred, but you are obliged to offer an expiation for an oath.

The permissible oath is to swear by Allah the Almighty. As for swearing by divorce, it is among the oaths of the transgressors.