A woman travelling with the son of her neighbour or the husband of her husband’s daughter
Question

                A woman wants to go and perform Hajj, although she has performed this obligatory duty before. Her stepdaughter will be going with her, and the husband of her stepdaughter. Is he regarded as a mahram for her, and is it permissible for her to travel with him?

 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?.
Praise be to Allah.
    Firstly: 

    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. 

    See question no. 316, 
    47029. 

    Secondly: 

    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 …”

    [al-Nisa’ 4:23]
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 
Thirdly: 
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? 
They replied: 
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]
End quote. 
Fataawa al-Lajnah 
    al-Daa’imah, 11/91.