Is the husband's statement: "By God, you will not return," considered a divorce or an oath requiring expiation, knowing that intercourse occurred after her return without his request?

Divorce occurs by the husband's intention. If he intended a divorce conditioned on his wife's return home, then as soon as she returns, the divorce takes effect. Writing is equivalent to verbal pronouncement. If he has intercourse with her before the 'iddah (waiting period) expires, she returns to his bond. However, if he did not intend divorce, then he must offer expiation for breaking an oath for her return. If he intended ẓihār (a pre-Islamic form of divorce by likening one's wife to a forbidden female relative), then it takes effect, and he must offer expiation for ẓihār.