What is the ruling regarding the brother, father, and son of the wet-nurse in relation to my wife, concerning the permissibility of shaking their hands, their seeing her hair, and being in seclusion with them? And is it permissible for them to perform Hajj with her as ahrim (mahram), knowing that my wife has suckled more than five satisfying breastfeeds from this woman?

If the woman mentioned is your wife’s foster mother, then her children are considered siblings to your wife, and her grandparents are considered her mahram (definition). They are permitted to see what mahram by lineage are permitted to see, and they are considered her mahram for travel; based on the Prophet’s (peace be upon him) saying: “Fosterage prohibits what lineage prohibits.”