Is it permissible for a wife to return to her husband who divorced her before consummation, then took her back and she bore him children, knowing that he divorced her after the children were born and both of them wish to reconcile?

A divorce before consummation is considered a minor irrevocable divorce (baynunah sughra). Returning to a divorced woman before consummation is only permissible with a new marriage contract. Your brother-in-law's cohabitation with your sister is considered a doubtful act (shubha), and any children born from it are attributed to him. They must be separated immediately. If he wishes to marry her, a new contract is essential. As for the second divorce that occurred, it is null and void because it did not apply to a valid subject.