Do her children from breastfeeding have any relationship with her second husband?

1 – When the infant has been breastfed by the woman five
times within the first two years of life, before weaning, then he becomes
her child through breastfeeding, according to the consensus of the imams,
and he becomes a mahram for her. The man to whom the milk belongs (because
he is the father of the child whose conception and delivery led to
production of the milk) becomes a father to the child through breastfeeding,
according to the consensus of the well-known scholars. This is proven
according to the Sunnah of the Messenger of Allaah (peace and blessings
of Allaah be upon him). 

2 – If the man and woman become parents of the child through
breastfeeding, then all their children become brothers and sisters to the
breastfed child, whether they are children of the father only (from another
wife) or of the mother only (from another husband) or from them both, or
they are their children through breastfeeding. They all become brothers and
sisters of this child through breastfeeding. Even if a man has two wives and
one breastfeeds a baby boy and the other breastfeeds a baby girl, these two
children become brother and sister and it is not permissible for them to
marry one another, according to the consensus of the four Imams and the
majority of Muslim scholars. Ibn ‘Abbaas was asked about this matter and
said: “The inseminator is one” – i.e., the man who had intercourse with both
women, which led to the pregnancies that produced the milk is one and the
same. 

3 – According to Muslim consensus, there is no difference
between the children of the woman who were breastfed along with this child
and those who were born to her before or after that. 

See Majmoo’ al-Fataawa, 24/31-32 

4 – There is no paternal relationship between the woman’s
children through blood or through breastfeeding and her second husband,
i.e., he is not regarded as a father to them through breastfeeding. The milk
belongs to the first husband, who is a father to all of them. But her second
husband is their mother’s husband and by his marrying her, her daughters by
blood become mahrams to him, because they are his stepdaughters (rabaa’ib),
and when he has consummated the marriage with their mother they become
mahrams to him. Allaah says (interpretation of the meaning): 

“Forbidden to you (for
marriage) are: … your stepdaughters under your guardianship, born of your
wives to whom you have gone in”

[al-Nisa’ 4:23]

With regard to the relationship between the woman’s daughters
through breastfeeding and her second husband who was not the owner of the
milk, and whether or not they are mahrams for him because he is the husband
of their mother – this is a matter concerning which there is a difference of
opinion among the scholars. 

The majority of scholars think that the woman’s daughters
through breastfeeding are mahrams for the second husband, because he is the
husband of their mother. Shaykh al-Islam Ibn Taymiyah was of the view, and
Shaykh Ibn ‘Uthaymeen agreed with him, that they are not mahrams for him. 

Based on this, the women who were breastfed by this woman
should observe hijab in front of her second husband, because he is not a
mahram for them. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: If
we examine the view of the majority, which is that it is not permissible for
him to marry his wife’s daughter through breastfeeding and the view of
Shaykh al-Islam Ibn Taymiyah that she is not a mahram for him, we may draw
the conclusion that we should err on the side of caution because that is the
approach that is referred to in the Sunnah. Sa’d ibn Abi Waqqaas disputed
with ‘Abd ibn Zam’ah concerning a slave of Zam’ah. Sa’d said: “O Messenger
of Allaah, this is the son of my brother ‘Utbah ibn Abi Waqqaas, whom he
entrusted to my care because he is his son.” ‘Abd ibn Zam’ah said: “This is
my brother, the son of my father’s slave woman who was born on my father’s
bed.” The Prophet (peace and blessings of Allaah be upon him) saw that
the child clearly resembled ‘Utbah but he said: “He is yours, O ‘Abd ibn
Zam’ah. The child belongs to the bed.” Then he said to Sawdah bint Zam’ah,
who was one of the Mothers of the Believers (the Prophet’s wives): “Observe
hijab from him, O Sawdah.” Al-Bukhaari, 2053; Muslim, 1457. Even though he
had ruled that he was a brother of hers, he told her to observe hijab from
him because he saw that he clearly resembled ‘Utbah. This was the ruling of
the Prophet (peace and blessings of Allaah be upon him) that was based
on erring on the side of caution. He told her to observe hijab because there
was some doubt about him, and he ruled that he was her brother because he
was born in her father’s bed. 

Duroos al-Haram al-Makki, vol. 3
p. 245. 

And Allaah knows best. 

For more information see question no.
40226.