Does the phrase "by the standing of my Lord" (Bajah Rabbi) constitute an oath necessitating fulfillment, and in the event of a wife's immediate non-compliance, is that considered a breach of the oath requiring expiation from the one who uttered it?

An oath is not constituted by the phrase "by the stature of my Lord" if its meaning is to swear by Allah, and there is no expiation upon the wife for not obeying her husband's command. It is recommended to fulfill a Muslim's oath to another if the matter is recommended or permissible, or if it involves abandoning something disliked or permissible. As for the "stature of Allah Almighty" in its original meaning, which is greatness, an oath can be made by it because it is an attribute of Allah Almighty.