Will a man be sinful if he divorces his second wife, whom he married secretly—especially since he knew her and committed fornication with her before the marriage—given that his father ordered him to divorce her, and he is unable to support two families, which forced him to take bribes?

Adultery is a grave sin, and the punishment for a married person who commits it is stoning. Those who commit adultery must repent, seek forgiveness, perform many good deeds, and not publicize their sin. Your secret marriage is valid if it met the conditions of marriage and the woman had repented and become righteous. You are not obligated to divorce her to please your father. However, if the woman is not righteous, it is preferable to divorce her, and this becomes more تأكد (confirmed/emphasized) if it is the wish of one of the parents. It may even become obligatory if you are unable to provide for her. Bribery is forbidden, and its perpetrator is cursed.