There is another scenario, which is a woman who is going to travel with her son, and her (female) neighbour wants to go with them. Is that permissible, knowing that the female neighbour is not a mahram for the son of her neighbour?.
In order for Hajj to be obligatory for a woman, she should have a mahram who can accompany her on her journey, because al-Bukhaari (1862) and Muslim (1341) narrated that Ibn ‘Abbaas (may Allaah be pleased with him) said: The Prophet (peace and blessings of Allaah be upon him) said: “No woman should travel except with a mahram, and no man should enter upon her unless she has a mahram with her.” A man said, “O Messenger of Allaah, I want to go out with the army for such and such (a campaign) and my wife wants to perform Hajj.” He said, “Go with her.”
Some scholars have granted a concession allowing a woman to travel for the obligatory Hajj with other women who are sincere and trustworthy, but this is a less correct view. The most correct view is that it is essential to have a mahram, whether that is for the obligatory Hajj or for a naafil Hajj.
Perhaps by “stepdaughter (rabeebah)” the questioner is referring to the daughter of her husband who is responsible for her.
The answer is that the stepdaughter’s husband is not a mahram for this woman, so it is not permissible for her to travel with him.
With regard to the “stepdaughter” mentioned in the verse where Allaah says (interpretation of the meaning):
“…your stepdaughters under your guardianship, born of your wives to whom you have gone in …”
this refers to the daughter of a man’s wife who was born to a man other than him (in a previous marriage). She is called rabeebah because the man brings her up (yurabbeeha) under his care… The fuqaha’ are agreed that the stepdaughter is a mahram for her mother’s husband if he has consummated the marriage with her, even if she is not under his care. Tafseer al-Qurtubi , 5/101
A woman has no right to travel with her female neighbour without a mahram. The son of her female neighbour is a not a mahram for her.
The Standing Committee for Issuing Fatwas was asked:
Can a woman perform the obligatory duty of Hajj with trustworthy women, if none of her family members are able to go with her, or her father is deceased? Can her mother, paternal aunt or maternal aunt accompany her in order to perform the obligatory duty of Hajj, or any person that she chooses to be her mahram for her Hajj?
The correct view is that it is not permissible for her to travel for Hajj except with her husband or a male mahram. It is not permissible for her to travel with trustworthy women or trustworthy men who are not her mahrams, or with her paternal aunt, maternal aunt or mother. Rather she must have with her her husband or a male mahram. If she cannot find anyone to accompany her, then Hajj is not obligatory for her because she is unable to meet one of the conditions. Being able to do Hajj is a necessary condition, as 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]
Fataawa al-Lajnah al-Daa’imah, 11/91.