Is the son obligated to abide by his father's oath after his death, in which he swore that the son's wife would not enter his house, despite the negative repercussions this would have on his son and his family life?

Fulfilling an oath is commendable but not obligatory. Therefore, there is no harm for a man to reside with his wife in the house he inherited from his father. What he inherited is not lost by his living elsewhere; he can claim it even after some time. A man can live with his wife and children in a rented or inherited house, so there is no justification for spouses to live separately.