Can I live with my mother after I swore, "The apartment is forbidden to me just as you, Mother, are forbidden to me," due to previous disagreements?

There is no harm in living with the mother. An expiation for an oath (kaffarat yamin) is required for making lawful things unlawful. Problems often arise between the husband's mother and his wife due to jealousy, and the husband must exercise wisdom to prevent Satan from exploiting the situation. The mother remains honorable and deserving of dutifulness, no matter how much she wrongs or falls short.