Is it permissible for my 54-year-old mother, who vowed to perform an 'Umrah, to go and fulfill her vow alone without a Mahram after my father's death?

There is no impediment to a woman traveling to perform the obligatory Umrah vowed as a

nadhr (vow) without a mahram, if she does not find a mahram, and she finds a safe companion group and is secure from fitnah (temptation/strife). This is the view held by some jurists, such as Malik and Al-Shafi'i. Ibn Taymiyyah said: "Every woman who is safe may perform Hajj without a mahram, and this applies to every journey undertaken for an act of obedience."