Is it impermissible to be intimate with a wife divorced once after a month has passed since the divorce, and what is the correct lawful way to take her back after the divorce took place in court and she is currently living with her family?

Scholars have differed regarding what is permissible for a man to do with his wife divorced by a revocable talaq (divorce), and by what means she is taken back. The preferred view is that a revocable talaq does not prevent enjoyment of the wife as long as she is in her iddah (waiting period); for she is like a wife, and she is entitled to the rights of a wife. And your cohabiting with her before the expiration of her iddah is considered taking her back if you intended intercourse. It is recommended to have witnesses to the reconciliation, and it is obligatory to declare the retraction before the court, stating the time when the retraction began.