Is it permissible for me to insist on not emigrating with my mother to a foreign country where there is corruption and where it is difficult to practice the religion, given my desire to remain with my father and relatives in Iraq? And if my mother insists on emigrating, is it permissible for me to go and live with my father, despite my fear that this might negatively affect my mother due to her sensitivity and intense dislike for my father?

If the reality is as you described, then there is no blame upon you for refraining from emigration, and disobeying your mother in this matter is not considered an act of disobedience (disrespect). There is also no blame upon you for moving to live with your father, and your mother's objection is not valid unless it has a justification. You bear no sin if she is harmed, provided it was not due to any negligence on your part. We advise you to be gentle with your mother, try to persuade her, counsel her with wisdom, and supplicate for her.