Is the wife considered sinful, and what can she do to win her husband back after her second divorce, especially given that she was forced to go out with her brothers, despite her husband's warning not to go out with them?

The marital life is a sacred bond and a solemn covenant. It must be held in high regard and not be exposed to weakness for the most trivial reasons. Problems and disagreements occur naturally, and the issue lies in not taking the time to resolve them. If a husband insults his wife in front of her family and abuses her, he is sinful and a wrongdoer. There was no need to rush in seeking a divorce due to the insult, as regret might result from it. The best recommendation is patience. There is no harm in seeking to return to the husband if this divorce is not the third one, and to seek help from Allah and from the wise members of the family. If the husband refuses, then do not exhaust yourself, for Allah may facilitate another husband for you, because, "And if they separate [by divorce], Allah will enrich each [of them] from His abundance. And ever is Allah all-Encompassing, all-Wise" (Quran 4:130). If the wife was harmed by the insult, she is permitted to seek a divorce. And if the insult was responded to in kind without exceeding the limit, then she is not sinful.