What should a man do who swore to his wife that she would never spend the night outside the home, then her mother died and she went to her family's home for condolences?

If by your statement "the oath is upon me" you meant an oath by Allah, and your wife defied you and spent the night outside her home, then an expiation for breaking an oath (kaffarat yameen) is incumbent upon you (feeding ten needy persons or clothing them, or fasting for three days).

However, if by "the oath" you meant divorce, then it is a divorce, and divorce here depends on your intention. If your intention was divorce, then it is a divorce, and if your intention was an oath by Allah, then it is an oath by Allah.

If you swore this oath without a specific intention, the preponderant opinion is that it is interpreted according to the prevailing custom in your country. So, if the custom dictates that it is a single divorce, then a single divorce is binding; if it is three, then three are binding. If it does not entail divorce, then an expiation for an oath is binding upon you.

The fatwa (definition) adopted by us is that an oath of divorce results in divorce upon its breach, whether the intention was divorce, or threat, or anything else.

If your wife spent the night outside the house and a divorce occurred, if it was the first or second divorce, you may take her back before her waiting period (iddah (definition)) expires. However, if it was the third divorce, she is not lawful for you unless she marries another man willingly, and then he divorces her or dies, and her waiting period expires.

It is known that a lawful oath is taken by Allah the Almighty, whereas an oath by divorce is one of the oaths of the dissolute.