Is the wife considered sinful for not communicating with her father, who disowned her and threatened to divorce her mother and deprive her sisters of education because she did not pay him a portion of her salary? What is the Sharia counsel in this situation?

If your father is in need of money, you must give it to him. If he is not in need, it is not obligatory, but giving it to him is considered an act of kindness, as long as it does not cause you harm. You must strive to honor him and be kind to him, while continuously trying to please him and seeking Allah's help. Your father's threat of divorce and depriving your sisters of education is impermissible, but that does not justify cutting ties with him or falling short in honoring him.