What is incumbent upon a female relative who vowed not to clean the house or work in its cleaning, then regretted it and wants to help her mother?

Your relative's vow not to clean the house is not a vow of obedience. Rather, it is a vow concerning something permissible, disliked, or forbidden. The majority of scholars hold that such a vow is not binding. Therefore, she may participate in cleaning the house, and there is no sin upon her. If she wishes to offer an expiation for an oath (kaffarat yamin) as a precaution, there is no harm in that.