What is the ruling on a man and woman remaining together as a married couple if the woman's father refuses to renew the marriage contract after a divorce in which no legitimate seclusion (khalwa shar'iyya) took place?

If the khalwa (private seclusion) was valid, such that intercourse could have occurred, then some scholars consider it to be tantamount to consummation (dukhool), and thus you may reconcile with your wife without a new contract. However, if a valid khalwa did not occur, then the woman is irrevocably divorced, and she cannot be taken back except with a new contract and mahr (dowry). She is considered a stranger, and it is not permissible to enjoy her before the contract. If the woman wishes to return, her guardian does not have the right to prevent her. If he prevents her without a valid reason, he is considered an ʿāḍil (one who obstructs marriage), and she may refer her case to a judge. It is advisable to present the matter to trustworthy scholars in the questioner's country.