Is it obligatory to obey the mother who commands not to listen to the father and not to clean the house in order to pressure him to take her back home, or to obey the father?

Both parents have a right to dutifulness and kindness. You must treat both your father and mother with kindness. You are not obligated to obey your mother if she forbids you from serving your father, for neither parent has the right to prevent their children from giving the other their due. Be careful not to disobey your mother by telling her what angers her. You should strive to reconcile between your parents by sending wise people, in fulfillment of the Almighty’s saying: "And if you fear dissension between the two, send an arbitrator from his people and an arbitrator from her people. If they both desire reconciliation, Allah will cause reconciliation between them. Indeed, Allah is ever Knowing and Acquainted [with all things]." And His saying: "And if a woman fears from her husband desertion or evasion, there is no blame upon them if they make terms of settlement between them - and settlement is best." And in the Hadith: "Reconciling disputes is better than the status of fasting, prayer, and charity."