What is the ruling regarding a man's statement to his wife in a state of anger: "By what is forbidden, if he [or it] enters the house in his [or its] direction [or, towards him/it]," and what is the expiation for this oath, knowing that he believed swearing by what is forbidden meant refraining from intercourse if the matter occurred?

As long as you did not intend divorce or ẓihār (a pre-Islamic form of divorce) by swearing by al-ḥarām (that which is forbidden), then the preponderant opinion according to us is that it requires an expiation for an oath (kaffārat yamīn) if you break it. The expiation for an oath is: feeding ten poor persons, or clothing them, or freeing a slave; and whoever cannot find [any of these] should fast for three days. It should be noted that the permissible oath is swearing by Allah, while swearing by divorce or al-ḥarām is forbidden.