Is the first return considered valid, with the wife still under the husband's marital authority, such that the second divorce, conditional upon a contingency, takes effect? Or has she been irrevocably divorced from him with a minor separation, and they are no longer spouses?

A divorce conditioned on a contingency does not take effect until the contingency occurs. Reconciliation is not valid except after the divorce has occurred. So, if the husband says, "Every time I divorce you, I have reconciled with you," and then divorces her, the reconciliation is not valid because it preceded the divorce. If the husband does not reconcile with his wife after the divorce takes effect and her 'iddah (definition) (waiting period) expires, she becomes irrevocably separated from him, and no divorce can subsequently occur after this irrevocable separation. Regarding conditional divorce intended for threat or emphasis, the majority of scholars hold that it takes effect, while some scholars, like Ibn Taymiyyah, are of the view that it does not take effect, and the one who breaks the oath must offer an expiation for an oath.