Is a divorce that was issued with a prior intention valid, then he retracted it after his anger subsided and he permitted his wife to do what he had sworn her against?

The husband's permission to his wife does not nullify a conditional divorce; the divorce remains valid. If the husband's intention behind the divorce was merely to prevent something, then he must offer expiation for breaking an oath (kaffarat yamin). However, if he intended to condition the divorce upon a specific action, then it occurs when that action takes place. If this divorce was not preceded by other divorces that would complete the count of three, it is a revocable divorce, and he can take her back during her waiting period ('iddah). But if it completes three divorces, then she becomes irrevocably separated from him (baynunah kubra) and is not lawful for him until after she marries another husband.