All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
It is unlawful, according to the Sharee'ah, for the Muslim woman to travel for a day and a night unless accompanied by a Mahram (a husband or a man who cannot marry her according to the Sharee'ah and she can uncover her face and head next to him and shake hands with him).
But, if the travel is obligatory, she is allowed to do it provided she is accompanied by a group of trustworthy women and does not fear temptation. This is the view of the Shaafi'i School of jurisprudence and it is the choice of Shaykh Ibn Taymiyyah .
If the woman in question is the only person who can take care of her mother and nobody else will do that job, then it is lawful for her to travel if there is no fear of temptation and if she is seen off at the airport of departure by a Mahram and met at the airport of arrival by another Mahram.
For more benefit on the prohibition for a woman to travel without a Mahram, please refer to Fataawa 262621, 88562, 193077, 102095, 83795 and 85945.
Allah knows best.