What is the recompense for a sister's husband who falsely swore on the Qur'an that he did not touch his sister days after their divorce, while his sister affirms that he did touch her, kiss her, and enjoy her without intercourse, all so that he would not have to take her back?

Your brother-in-law's oath is one of two things: Either he is truthful, in which case he should be believed, for the Prophet, peace and blessings be upon him, said: "Whoever is sworn to by Allah, let him be satisfied." Or he is a liar, and his oath is a false oath (yamin ghamus) for which he deserves disciplinary punishment in this world. Since the case has been presented to the judge, he is most entitled to rule on it based on the evidence presented to him.