Is it permissible to take back one's wife after divorcing her twice, knowing that she has not yet completed her 'iddah (waiting period prescribed by Islamic law)?

Your divorce of your wife online in writing is considered a metaphorical divorce, which takes effect if you intended it to. Your resumption of conjugal relations with her after the divorce is valid if it was before the expiration of her waiting period (iddah). The second divorce that occurred during anger is effective if you were aware of what you were saying, and you may resume conjugal relations with her before the expiration of her iddah without a new contract. However, if your anger was so severe that you lost consciousness, then nothing is incumbent upon you.