Does a father sin by divorcing his wife due to his daughter's interventions, and does the daughter sin for her actions, and does the saying "He who is silent about the truth is a mute devil" apply to the brother who did not intervene?

Islam encourages reciprocating kindness with kindness, especially when the kindness originates from the other party. Therefore, the sister should treat her stepmother with similar or even greater kindness. It is not permissible for her to restrict her stepmother's expenses, clothing, or housing, nor to pry into matters her stepmother wishes to keep private, nor to do anything that would cause separation between her stepmother and her husband. If she does any of these things, she incurs sin.

As for the questioner, she must advise her sister and prevent her from interfering in impermissible matters, in accordance with the hadith (definition): "Whoever among you sees an evil, let him change it." If she fulfills her duty, she bears no sin. There is also no sin upon the father for agreeing to the divorce his wife requested, unless he was negligent in his duties.