Should she go with her mother for ‘Umrah without a mahram or stay at home on her own?

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. 

.End quote. 

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.