Is a wife entitled to seek khul' due to a minor dispute that led to her leaving the marital home, followed by her being issued one divorce pronouncement and then taken back?

It is not permissible for a woman to leave her husband's house without his permission, except out of necessity. If the relationship between the spouses deteriorates, an arbiter from his family and an arbiter from her family should intervene to reconcile them. If the wife dislikes her husband, she has the right to seek khul' (divorce at her initiative, typically by returning the dowry). If you took your wife back before the expiry of her iddah (waiting period), then she is obliged to return. If she dislikes you, you have the right to refuse to divorce her until she forfeits some of her rights. It is preferable for wise people to mediate. If the wife wishes to return and her father prevents her, then he should not be obeyed, for her husband has a greater right to her, and obedience to him is more obligatory.