Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
According to the majority of scholars, a husband does not have the right to prevent his wife from performing the obligatory hajj and he becomes sinful if he does so.
Answering your question, Dr. Muhammad Salama, PhD, Islamic Studies in English, Associate Professor at the Faculty of Islamic Sciences al-Madinah International University (Mediu), states:
A husband may not prevent his wife from performing the obligatory Hajj as long as she has fulfilled all the required conditions.
According to the majority of scholars, a husband does not have this right and becomes sinful if he prevents his wife from fulfilling the personal obligation of hajj.
But if a wife wants to perform a voluntary hajj, then her husband has the right to prevent her since his permission in this case is a must.
Almighty Allah knows best.