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. We ask Allaah to exalt his mention as well as that of his family and all his companions.
There is no doubt that pleasing the parents is one of the reasons of entering paradise. The Prophet said: "The pleasure of Allaah is attained by pleasing parents, and the wrath of Allaah is ensued by angering parents." [At-Tirmithi] However, this does not mean that a person should not advise his parents or admonish them to do good and forbid them from doing evil out of fear of angering them. Rather, it is an obligation on the son [or daughter] if he sees his mother or father committing a sin, like backbiting and the like, to forbid them from doing so, with good and soft words and in a manner that befits their status as parents as long as they do not get angry. When they get angry, he is obliged to keep quiet. Forbidding them from doing evil is considered as an act of being kind and dutiful to them because this is a reason of saving them from the fire. Indeed Allaah, the Exalted, informed us how the Prophet Ibraaheem (Abraham) advised his father in good and soft words. Allaah Says [reporting the words of Ibraaheem] (which means): {O my father! Do not worship [i.e. obey] the devil. Indeed the devil has ever been, to the Most Merciful, disobedient. O my father! Indeed I fear that there will touch you a punishment from the Most Merciful so you would be to the devil a companion [in Hellfire].}[Quran 19:44-45]. There is no doubt that speaking about other people and backbiting them is one of the great major sins. Whoever has done so is obliged to repent to Allaah. Similarly, the person who hears others backbiting people is obliged to forbid them from backbiting, and he should remind them about the right of Allaah on them and that they are obliged to repent. Besides, one should remind them about the danger of backbiting and its evil fate in this world and in the Hereafter. It is confirmed that the Prophet said: "Whoever sees an evil, should change it with his hand (i.e. physically); if he can't, then he should change it with his tongue (i.e. verbally); if he can't then he should reject it in his heart (i.e. detest it), and this is the weakest level of faith." [Muslim]
Therefore, we advise you, dear sister, to forbid your father from backbiting other people with words and expressions that suit his status as a father. If he takes heed, then all perfect praise be to Allaah, otherwise you have done your duty of enjoining good and forbidding evil. However, if you know that forbidding him from doing so will anger him, then you should be silent [refrain from forbidding him] and not anger him; this is the view of the scholars.
Allaah Knows best.