Everyone wants their family to be happy, and they don't want differences between their parents, let alone seeing either of them cheat.
But wishes are always good. If you find out that your father has a mistress, I think you can deal with it in the following ways:
First, make an appointment with your father for a private chat.
Everything happens for a reason, and everything that happens has an unknown story behind it. Whether there are contradictions or differences in married couples' life, you can probably have a very intuitive understanding in your usual family life. You can ask your father out alone to communicate, ask the situation directly in person, understand your father's thoughts, or learn about the life between parents from your father's mouth.
Besides, you can also express your attitude and make your thoughts clear to your father to alert him.
second: keep the evidence that your father has a mistress.
If your father doesn't want to admit that he has a mistress, and you don't want to tell your mother anything, then you'd better keep the evidence of finding out that your father has a mistress and expose him in front of your father alone. This will not only leave a sense of dignity for my father, but also prevent the contradiction between my parents because of the mistress.
If your father is still unwilling to repent in the face of evidence, the evidence in your hand is the best protection for you and your family. Since your father is willing to abandon his family for a mistress, there is nothing to be polite to him. It is time to go through legal procedures.
Third, be a bridge between mom and dad.
Dad has a mistress, it must be because of the emotional problems between him and his mother. You can play a good regulatory role in the middle. For example, you can tell each other about their needs and finally find a compromise.
No one wants a third party in the family, but since there is a problem, try to solve it.