What should I do about my knowledge of my mother's betrayal of my father over the phone; should I tell my father and ruin the home, or should I keep silent and bear the pain?

If you are certain about what your mother is doing, then you must advise her gently and kindly, explaining to her that what she is doing is a great sin, and warning her of the consequences of that. You should show her your concern and fear for her, following the example of Ibrahim's advice to his father. If she does not respond, repeat the advice, and make her fear the news reaching your father without explicitly stating it. If nothing works, then subtly alert your father to look after his household, in order to avert the greater of two evils. And do not forget to persistently pray for her guidance during times when prayers are answered.