Does divorce occur and entail expiation after saying to a wife who did not comply with a request, "By divorce, you will not enter her house again," knowing that the wife is currently visiting her relative?

Your oath of divorce is a binding oath according to the majority of scholars. The way to prevent the divorce from occurring is for your wife not to visit that relative in her house. If she visits her, divorce will occur according to the majority. Sheikh al-Islam Ibn Taymiyyah is of the opinion that you are liable for an expiation for an oath if you did not intend divorce, and that you can retract this condition.

According to the madhhab of the majority, if your wife visits her relative, divorce occurs and the oath is dissolved. You can then take your wife back before her 'iddah ends, provided this is not the third divorce. Nothing is binding on you if you were not aware of what you were saying at the time of the oath due to extreme anger.