Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
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:
1- The principle in Shari`ah is that a woman is not to travel by herself; rather, it is obligatory for her to be accompanied by her husband or a mahram (close male relative).
2- Since the true intent of the prohibition is safety and protection, she is allowed to travel in a safe company accompanied by reputable Muslim men and women.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
It is permissible for your mother to go for Hajj if she can travel in a safe company where she can feel reasonably secure and protected.
Islam is a religion that is wholly based on mercy and compassion. Its teachings are aimed at protecting the weak and the vulnerable.
It is, therefore, with the specific intent of safeguarding a woman’s honor, dignity, and reputation that the Prophet (peace and blessings be upon him) forbade women from undertaking long journeys without a mahram.
Since the true intent of the prohibition is safety and protection, women are allowed to travel in a safe company accompanied by elders and reputable Muslim men and women.
That is why we read in the sources that the Mothers of the Faithful such as `A’ishah and Umm Salamah, themselves well known for their deep knowledge of Islam and expertise in Islamic jurisprudence, traveled without mahrims in a safe company.
They traveled in a group under the protection of older men. Once `A’ishah was asked whether a woman can travel without a mahram. Her answer was, “Can everyone find a mahram?”
In other words, if she has a genuine need to travel, she may do so if she can be reasonably assured of her own safety.
Based on the above considerations, a number of jurists and scholars belonging to the Maliki and Shafi`i schools, as well as others, have considered it permissible for women to travel in a safe company.
Therefore, your mother is allowed to travel with her cousin and her son, provided she is part of a larger group consisting of other men and women of sound reputation.
Allah Almighty knows best.
Excerpted, with slight modifications, from: www.islam.ca