Does a woman have the right to seek divorce from her husband whom she describes as manipulative and unclear, and whom she deeply regrets marrying, especially since she fears for her daughter from the influence of her husband's daughter who is unaware of things she should not know about Islam and who hates Arabs, and she feels that God might punish her if she upsets him?

Your actions of seeking divorce from your former husband without a valid reason, and entertaining marriage proposals while still married to him, are sins that require repentance. Affection is not a prerequisite for the stability of marital life, and it is forbidden to propose marriage to a married woman, even indirectly. Now, after the divorce and your current marriage, live with your husband in kindness and cooperate in obeying Allah. Strive to raise your daughter and his son upon virtues. Divorce should only be resorted to after all attempts at reconciliation have failed, and it is not advisable to seek it unless the husband is neglectful of Allah's obligations or clearly oppressive.