Is the return (reconciliation) valid after a conditional divorce, following the wife's departure to her family's home? Is it a condition to prove the divorce and the return (reconciliation) in court? And what should I do if the father refuses to hand over my wife after she has given birth?

If the husband takes his wife back during her iddah (waiting period), the revocable return (raj'ah) is valid, and neither the wife nor her guardian has the right to refuse it. However, if the return is after the iddah has ended, the wife has the right to refuse it, unless the husband brings proof that he took her back during the iddah. Her word is to be accepted unless the husband provides evidence to confirm his claim.

So, if the communication in which the husband informed his wife of the return occurred during the iddah, the return is valid. But if it was after its expiration, and the wife denies it, she has the right to refuse unless the husband proves his claim with evidence.