What is the legitimate and religiously permissible solution and treatment for dealing with a father's sexual harassment of his daughter, where he touched her chest and other sensitive areas?

Your father committed a grave act by violating both religious law (Sharia) and natural inclination (fitra). If it is forbidden with a stranger, then with a mahram it is more severe and greater, as the Prophet, peace and blessings be upon him, said: "Whoever has intercourse with a mahram, kill him." Therefore, he must repent. You must advise him and prevent him from being alone with your sister, and seek help from people of sound judgment and righteousness, while still treating him with kindness.