A woman who cannot find a mahram to travel with her is not obliged to do Hajj or ‘Umrah; she is excused for not doing that, and it is haraam for her to travel for Hajj or for any other reason without a mahram. She has to be patient until Allaah makes available a mahram with whom she may travel.
There are many ways of doing good. If a Muslim cannot do some acts of worship, then he should strive hard in those acts of worship that he is able to do, until Allaah makes it easy for him to do the acts of worship that he is unable to do.
By the grace of Allaah towards His believing slaves, if a person resolves to do an act of worship but he is not able to do it for some reason, He will still reward the person for it. al-Bukhaari (4423) narrated from Anas ibn Maalik (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him) came back from the campaign to Tabook and when he drew close to Madeenah he said: “In Madeenah there are people who, whenever you travelled any distance or crossed any valley, were with you.” They said: O Messenger of Allaah, even though they are in Madeenah. He said: “Even though they are in Madeenah, because they were kept there by excuses.”
It says in Fataawa al-Lajnah al-Daa’imah (11/90):
A woman who does not have a mahram does not have to do Hajj, because in her case a mahram is part of being able to do Hajj, and being able to do it is one of the conditions of Hajj being obligatory. Allaah says (interpretation of the meaning):
“And Hajj (pilgrimage to Makkah) to the House (Ka‘bah) is a duty that mankind owes to Allaah, those who can afford the expenses (for one’s conveyance, provision and residence)”
[Aal ‘Imraan 3:97]
It is not permissible for her to travel for Hajj or for any other purpose unless she is accompanied by her husband or a mahram, because of the report narrated by al-Bukhaari and Muslim from Ibn ‘Abbaas (may Allaah be pleased with him), that he heard the Prophet (peace and blessings of Allaah be upon him) say: “No man should be alone with a woman unless her mahram is present, and no woman should travel unless she has a mahram with her.” A man stood up and said: “O Messenger of Allaah, my wife has gone out for Hajj, and I have enlisted for such and such a campaign.” He said: “Go and do Hajj with your wife.” This was also the view of al-Hasan, al-Nakha’i, Ahmad, Ishaaq, Ibn al-Mundhir and ashaab al-ra’i, and it is the correct view, because of the verse quoted, as well as the general meaning of the ahaadeeth which forbid a woman to travel without her husband or a mahram. Maalik, al-Shaafa’i and al-Awzaa’i held a different opinion and each of them stipulated a condition (allowing her to do that), but with no evidence. Ibn al-Mundhir said: they did not follow the apparent meaning of the hadeeth, and each of them stipulated a condition (allowing her to do that), but with no evidence.
Just as it is not permissible for a woman to travel without a mahram, it is not permissible for her mother either. She should fear Allaah and stay with her daughter. If she insists on going and that results in the daughter staying alone, then if she is staying in a safe place there is no problem, but if she is afraid of staying alone, then this may be an excuse for her to go with her mother as a case of necessity, and the sin will be on her mother.
And Allaah knows best.