Praise be to Allah.
If the wife’s father was breastfed by his sister and it was five full breastfeedings within the first two years, then he becomes a son to her through breastfeeding, and her children, both males and females, become siblings to him through breastfeeding; they become paternal uncles and aunts to his children through breastfeeding. Thus it is proven that the relationship of mahram exists between them.
The basic principle concerning that is the verse in which Allah says (interpretation of the meaning):
“Forbidden to you (for marriage) are: your mothers, your daughters, your sisters, your father’s sisters, your mother’s sisters, your brother’s daughters, your sister’s daughters, your foster mothers who gave you suck, your foster milk suckling sisters”
So the daughter of a brother through blood ties is a mahram.
And the Prophet (blessings and peace of Allah be upon him) said: “What becomes mahram (forbidden for marriage) through breastfeeding is that which becomes mahram through blood ties.”
Narrated by al-Bukhaari, 2645; Muslim, 1447..
So the daughter of a brother through breastfeeding also becomes a mahram.
The scholars of the Standing Committee for Issuing Fatwas said:
The breastfeeding which establishes the relationship of mahram is that which takes place five or more times in the first two years. If the breastfeeding of the two brothers was like this, then they are brothers through breastfeeding and the children of each of them are the children of his brother through breastfeeding. … And it is not permissible for one of them to marry the daughter of the other, because they are his nieces (children of his brother) through breastfeeding. End quote.
Fataawa al-Lajnah al-Daa’imah, 21/116
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked:
I was breastfed with my maternal uncle by my grandmother – who is his mother. Should my daughters observe hijab in front of him, knowing that I was breastfed more than five times?
If you were breastfed by your grandmother with five certain breastfeedings, then you became a child to her, and her children are your siblings, both the older and younger ones among them. If they became your brothers, they became paternal uncles to your daughters. Based on that, it is permissible for your daughters to uncover in front of all of their maternal uncles. End quote.
Liqa’ al-Baab al-Maftooh, 40/8
Based on that, your wife may shake hands with the sons of this woman and uncover her hair in front of them, because they are her paternal uncles through breastfeeding.
And Allah knows best.