Praise be to Allah.
Asking husband’s permission for obligatory Hajj
If Hajj is obligatory for a wife and her husband tells her not to go, she may do Hajj even if her husband has not given her permission . It is not permissible for the husband to forbid her to go for the obligatory Hajj.
Asking husband’s permission for voluntary hajj
But if it is a nafl (voluntary) Hajj, then she should not go for Hajj without her husband’s permission.
Ibn Qudamah (may Allah have mercy on him) said in al-Mughni (5/35):
“A man does not have the right to forbid his wife to do the “Hajj of Islam” (i.e., the obligatory Hajj). This is the view of al-Nakha’i, Ishaq, Abu Thawr and ashab al-ra’y, and it is the correct one of the two views of al-Shafi’i. This is because it is obligatory and he has no right to forbid her to do it, as is also the case with the fast of Ramadan and the five daily prayers. But it is mustahabb for him to ask his permission for that. This was the view of Ahmad. If he gives her permission, all well and good, otherwise she may go without his permission. In the case of a voluntary Hajj, he has the right to forbid her.
Ibn al-Mundhir said: All the scholars from whom I have learnt unanimously agreed that he has the right to forbid her from going for a voluntary Hajj. That is because the husband’s rights are binding, and she does not have the right to ignore them for something that is not obligatory.”
Can a husband prevent his wife from making Hajj?
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) was asked: If a husband forbids his wife (from going for Hajj), is he sinning?
“Yes, he is sinning if he forbids his wife from going for Hajj when she has met the conditions (of it being obligatory). If she says, “Here is my mahram , he is my brother who will take me for Hajj, and I have enough money and I do not want a penny from you,” and if she has not yet performed the obligatory Hajj, then he must give her permission. If he does not, then she may go for Hajj even if he did not give permission, unless she fears that he will divorce her, in which case she is excused.” (Fatawa Ibn ‘Uthaymin, 21/115)
And Allah knows best.