Is a wife forbidden to her husband who divorced her twice, intending the second divorce to confirm the first, then took her back and had relations with her, then divorced her a third time?

The second divorce does not take effect if it occurs during the waiting period (iddah), and this is the most preponderant opinion, and that a divorce only takes effect if it is preceded by a reconciliation or a marriage contract. So, if a man divorces his wife and then divorces her again during the iddah before taking her back, nothing but the first divorce is counted against him.