Is a wife considered divorced if her husband breaks an oath of divorce—specifically, that he would not pick her up from work while she was menstruating—and both of them had forgotten the oath when the breach occurred?

Doing the sworn-upon act out of forgetfulness does not harm, and it does not result in a broken oath or divorce, because of the Prophet's (peace be upon him) saying: "Verily, Allah has pardoned for my Ummah their mistakes, their forgetfulness, and what they are forced to do." So, as long as the husband accompanied his wife forgetful of his oath, no divorce takes place upon him.