Aunt Jane's Nieces by L. Frank Baum

Jane Merrick is a wealthy, elderly, difficult invalid woman who is preparing for her approaching death. In her youth, she inherited her money and estate from her fiancé, Thomas Bradley, who died before their wedding took place. With no children of her own, she calls for her three teenaged nieces to visit her, so she can decide who will inherit her estate. They are Louise Merrick, Elizabeth De Graf, and Patsy Doyle, children of Jane's younger brother and sisters. Each of the three cousins is a different type.