I don’t understand what you mean about what happens if “her” is left out of the sentence at the top of the page, “There would be no one to live for her during those coming years; she would live for herself.” How does including “her” change the meaning of the sentence?
A: Without “her,” the sentence means that Louise Mallard has been living for her husband, that he has been the center of her life, that he has been her reason for living. With “her,” the sentence means that Brently Mallard has been controlling his wife’s life, that his “powerful will [has been] bending hers” to his, has been bending what she wants to what he wants, has been forcing her to live the way he wants her to live, to do what he wants her to do.
That’s an important distinction. “Her” in the sentence explains what Mrs. Mallard means by her newly recognized “possession of self-assertion,” what she means by whispering, “Free! Body and soul free!”