Is it permissible for a mother to threaten her daughter with complaining to Allah because the daughter refuses to apologize to her sister, knowing that the daughter feels her sister harbors resentment towards her?

You should have thought well of your sister and avoided words that incite discord, for Satan sows dissension among people. Obey your parents, apologize to your sister, and strive against the whisperings of Satan. If your sister wrongs you, repel the evil with good and kind words, for forgiveness increases your honor and breaks enmity.