Is it permissible for the wife to drive a car for the benefit of the family, given that the father stipulated before marriage that she not drive and the husband agreed, then his opinion changed due to an extreme necessity?

Fulfilling the conditions of marriage that do not contradict the essence of the contract is obligatory, and this condition seems to be for the wife's benefit. If the wife is an adult of sound judgment and waives her right to this condition, then it is dropped. Sheikh Muhammad ibn Ibrahim Al ash-Sheikh was asked about stipulating that the wife remain in her country and not move with the husband. He replied that the condition is valid and binding, based on the hadith: "Indeed, the most worthy of conditions to be fulfilled are those by which you have made lawful intimate relations." However, if the wife agrees to move, the right is hers, and if she waives it, it is dropped. If there is a dispute, the matter should be referred to the Sharia court. It is preferable to try and convince the father through the mediation of good-willed people to avoid conflict.