Is the mother considered divorced because the son entered the house after the father swore an oath to that effect? And what is the way to settle disputes and mend the family relationship?

You must mend your relationship with your father, as honoring one's parents is one of the greatest duties. If you entered the house with your mother's knowledge and consent, then the divorce is effective, and one divorce will have occurred, unless your father intended more than that. Inform your father of what happened so he can review his wife's situation. If the divorce occurred, then the oath has been dissolved, and divorce will not occur again if you enter the house another time.

All of this is according to the majority of scholars who state that divorce occurs if the condition it was contingent upon is met. However, according to the school of thought of Sheikh al-Islam Ibn Taymiyyah, if your father intended divorce if the entry occurred, then the previous ruling applies. But if he did not intend to effect a divorce, but rather intended to prevent her from bringing the child into the house, then he is liable for an expiation for breaking an oath, and no divorce is counted against him.