Can the aforementioned husband, who irrevocably divorced his wife in absentia and then had intercourse with her, believing that his brother had taken her back after the 'iddah (waiting period) had expired, return to his wife after her arrival in America?

If your brother divorced your wife after you appointed him as your agent, and neither you nor he took her back until her waiting period (iddah) expired, then she has become irrevocably separated from you. If the divorce was less than three pronouncements, then it is permissible for you to remarry her with the consent of her guardian and the testimony of two witnesses. However, if this was the third pronouncement of divorce, then she has become irrevocably separated from you with a major separation (baynunah kubra), and she is not lawful for you unless she marries another man willingly, he consummates the marriage with her, and then he divorces her or dies, and her waiting period from him ends.