Is the statement, "By Allah, my family will not reside in this house even if the entire deal is ruined," considered an oath, and what are the implications if one wishes to retract this decision by returning to the family home?

What was uttered is not considered an immediate or conditional divorce; rather, it is merely a hypothetical assumption of the possibility of a future separation. As for confirming that the wife will not return to the family home by an oath, this is a binding oath (yameen mun'aqidah) for which expiation (kaffarat yameen) is due if it is broken. It is advised to balance obedience to parents with the rights of the wife, knowing that living separately from parents does not negate filial piety. It is the wife's right to have an independent dwelling with private facilities.