Is the divorce of a wife who requested divorce and agreed to absolve her husband of half of the deferred dower considered a revocable divorce, allowing the husband to take her back during the iddah (waiting period), or an irrevocable divorce?

If you divorce your wife in exchange for her relinquishing half of the deferred dower, this is an irrevocable divorce [talaq ba'in], and you cannot take her back except with a new contract. It is advisable to present the matter to the Sharia court or to trustworthy scholars for clarification and a fatwa.