To what extent does a wife have the right to intervene in her husband’s spending on his family, especially if these expenses fall within the scope of luxuries or extravagance? And is her discussion of previous annoyances from her husband’s family considered backbiting (gheebah)?

If the husband spends reasonably, then the wife has no right to object to his spending on his family. However, she can gently and wisely advise him to balance his spending on his family with saving money for his household. What the wife mentioned regarding the ill-treatment by her husband's family is not backbiting (gheebah) that is forbidden if it is for a legitimate interest. Among the beautiful aspects of marital life is for each spouse to treat the other's family kindly, help them honor their parents and maintain ties with their kin, and overlook their shortcomings.