Your wife has misunderstood the Islamic rule in this matter. Mahram is the person who is permanently forbidden for marriage with her under any circumstance for life e.g. her real brother , real uncle, real father, father in law, her son and son in law. Her sister's husband is not permanently forbidden to marry her, but only when her sister is his wife. If she dies, God forbid, or if she is divorced from him, marriage will be then allowed between this man and any of the unmarried sisters of his ex-wife.
Her sister's husband is not Mahram at all and must observe full Hijab in front of him like any other non Mahram man.