What is the ruling on a husband preventing his wife from communicating with her sister in the the name of her sister's husband, and is the wife permitted to refuse that on the grounds of her familiarity with the caller?

Couples are required to foster understanding and respect, and to avoid doubtful situations. Muslim men and women should stay away from anything that necessitates an apology. Al-Tabarani narrated from Ibn 'Umar, may Allah be pleased with them both, that the Prophet, peace and blessings be upon him, said: "And beware of that for which you have to apologize." It is narrated in Sahih al-Bukhari the story of Safiyyah, the wife of the Prophet, peace and blessings be upon him, and his saying: "Indeed, Satan flows through the son of Adam like blood, and I feared that he might cast something into your hearts." Al-Nawawi said: "This indicates the desirability of guarding against exposing oneself to people's ill suspicions, seeking safety, offering valid excuses, and clarifying the situation to dispel ill suspicions." If the husband knows the identity of the caller, others may not, and Satan may cast doubts into the husband's heart.

The appearance of the brother-in-law's name, to someone unaware that the caller is the sister herself, might lead to ill suspicions about the wife. This necessitates preventing it, and she must obey her husband in this matter.