Is a divorce effected by the husband's saying to the wife's father, "I have divorced your daughter," given that he later denies saying it and claims he did not intend divorce, and the father confirms he did not hear the word of divorce from him? And is the wife considered disobedient if she leaves the marital home in this situation?

The statement your husband made does not result in a divorce; rather, it is merely a promise of divorce, and divorce does not occur simply by promising it. Furthermore, if his informing your father that he divorced you was a lie, then his divorce is not religiously valid. Consequently, you are still under his marital bond, and you are obligated to obey him and live with him amicably.