Is it permissible for me to inform my brother about his wife's transgression against my parents, knowing that he might take a firm stance that could lead to her divorce or her going to her family's house?

It is advisable to counsel the wife that her actions of disrespecting and harming her husband's parents are forbidden, and she must respect them. If she responds positively, you are spared the burden of informing her husband. But if she insists, then inform someone who has the authority to admonish her, such as her father or brothers. If that does not work, there is no harm in informing the husband, even if it leads to divorce; for there is no good in keeping a wife who disrespects his parents.