All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
There is no doubt that backbiting Muslims is forbidden and it is even more forbidden to backbite the people of excellence amongst them especially the scholars. Ibn Asaakir said: “The flesh of the scholars is poisonous, and the manner with which Allaah exposes those who seek to belittle them is well known.” For more benefit, please refer to Fatwa 81748.
Therefore, if your father and your father-in-law degrade them, then they are committing a grave sin, and it is an obligation to forbid them from doing so, but this should be in a nice and soft manner especially when forbidding the father as we clarified in Fatwa 90818.
Indeed, we have mentioned in this above Fatwa that if advice to your father is of no avail, then praise be to Allaah, and if disapproving of him leads to angering him, then you should not do so.
Moreover, you should depart from the place in which there is backbiting and you should act in a wise manner because it is not permissible for a Muslim to stay in a place where Allaah is being disobeyed; Allaah Says (what means): {And when you see those who engage in [offensive] discourse concerning Our verses, then turn away from them until they enter into another conversation. And if Satan should cause you to forget, then do not remain after the reminder with the wrongdoing people.}[Quran 6:68]
Allaah Knows best.