Is it permissible for a woman to learn to drive without her husband's knowledge, given his refusal, and considering that she needs to drive to secure her transportation and that of her children, and to avoid relying on others?

A wife is not permitted to work outside her home except under certain conditions, including her husband's consent, and that her work does not prevent her from fulfilling her duties. The primary duty of a woman is to care for her home, children, and husband. If the husband forbids his wife from going out to work or to learn driving, it is obligatory for her to obey him, based on the Prophet's (peace and blessings be upon him) saying: "If I were to command anyone to prostrate to anyone, I would have commanded a woman to prostrate to her husband." Therefore, it is not permissible to learn how to drive a car without the husband's knowledge or to continue in a job if he disapproves. It is the husband's duty to provide for his wife in a reasonable manner.