What is the ruling regarding two sisters agreeing that each of them will nurse the other's child five times to establish mahramiyyah between the two children, without the knowledge of either husband, and what are the consequences of that?

There is no objection to nursing a niece or to a sister nursing one's son with the intention of establishing mahramiyyah, provided certain conditions are met: First, there must be five or more nursing sessions, based on the hadith of Aisha: "Ten known sucklings make one mahram," then this was abrogated by "five known sucklings." Second, the nursing must occur within the first two years of the child's life, based on the hadith: "There is no nursing [that establishes mahramiyyah] except what tears the intestines [i.e., satisfies hunger]." One nursing session is defined by the child latching onto the breast, sucking, and then releasing it voluntarily. If these conditions are met, the niece becomes your daughter through nursing and a sister to your children, and your son becomes a brother to his aunt's children.