Is the wife's return home during the day, after the husband said, "By divorce, you shall not stay in the house," considered a breach of the oath, knowing that she spent the night outside?

What is considered in breaking an oath is the intention and purpose of the swearer. The intention specifies the general and restricts the absolute. If you intended to prevent your wife from staying overnight for a specific period, there is no breaking of your oath if she returns after that period. Or if you intended to prevent her from staying overnight without her remaining during the day, then you do not break your oath by her entering the house during the day. It is best to consult scholars to understand the details of your intention. It must be noted that the permissible oath is by Allah Almighty, whereas swearing by divorce is among the oaths of the wicked and should be avoided.