Is it permissible for a husband to pay for an 'Umrah for his second wife without the knowledge of his first wife, and would this be considered a lack of justice?

It is permissible for a man to pay for the 'Umrah expenses of his second wife without the knowledge of his first wife, and this is not considered an act of injustice. This is because the obligatory justice is only in lodging, housing, sustenance, and clothing. As for anything other than that, he may exclusively give to whomever he wishes whatever he wishes. The majority of scholars have permitted a husband to favor one of his wives over another in non-obligatory sustenance and clothing, provided he has fulfilled the obligatory provisions for each of them. Ibn Qudamah narrated from Ahmad the permissibility of favoring one of them over the other in sustenance, desires, and clothing, as long as the other is sufficiently provided for.