Is it permissible to leave the wife and children with the wife's father after the repeated problems he instigated and his attempts to separate the spouses?

Your wife's father has no right to prevent her from returning to you, and she is not permitted to obey him in that. Rather, it is obligatory for her to return to you unless she has a valid excuse. Ibn Taymiyyah said: "When a woman marries, her husband has more authority over her than her parents, and obedience to her husband is more incumbent upon her." Al-Mardawi said: "She is not obliged to obey her parents in separating from her husband, nor in visiting [them] or similar matters. Rather, obedience to her husband is more rightful." It is advisable to seek the mediation of righteous people to facilitate the return of your wife and children, and if that does not work, then the matter should be brought before the judiciary.