Is it permissible for the husband to use a recorded phone call, overheard without the speakers' knowledge, to prove the ill intent of his wife and her family?

If the husband recorded the words of the wife's family without their knowledge, this is forbidden espionage, and he must delete the recording. If the wife's family spoke ill of him and his family, this is backbiting (gheebah) or slander (buhtan), which is forbidden, and everyone must repent. It is advisable to continue reconciliation between the spouses, as separation is among the deeds most beloved to Iblis.