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

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.