Am I obligated to divorce my wife because of her disagreement with my mother and sister and her hatred for them, which puts me in a dilemma?

You should not divorce your wife merely due to disagreements between her and your mother or sister, because divorce is disliked when there is no need for it, and it may even be forbidden due to the harms that result from it. Therefore, strive to reconcile between the parties, as this is one of the best acts of nearness [to Allah]. Seek out the causes of the disagreement and address them. Be just to the oppressed and prevent the oppressor from injustice, as stated in the Hadith: "Support your brother, whether he is an oppressor or oppressed... by restraining him, or preventing him from injustice; for that is supporting him." Keep your wife as long as she is righteous, and do not resort to divorce unless all avenues for resolution are blocked and the benefit of divorce outweighs other considerations.