Praise be to Allah.
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allaah have mercy on him) said: “Before replying, I would like to point out that it is not permissible for a woman to go out without her husband’s permission, even if that is in the same city, so how can she go for Hajj without his permission? This is haraam and it is not permissible for her to do this. The husband who promised to take his wife for Hajj has to fulfil his promise and take her for Hajj, especially since this promise is stated as a condition in the marriage contract. The Prophet (peace and blessings of Allaah be upon him) said: “The most deserving of conditions to be fulfilled are those by means of which intimate relations become permissible for you.” Narrated by al-Bukhaari, 2729; Muslim, 1418.
If this promise was made after the marriage contract, the scholars differed as to whether it should be fulfilled. The correct view is that it must be fulfilled so long as that will not cause harm to the one who made the promise, because the Prophet (peace and blessings of Allaah be upon him) described breaking promises as one of the attributes of the hypocrites, as a warning against breaking promises.
See Daleel al-Akhta’ allati yaqa’ fiha al-Haaj wa’l-Mu’tamir.