Love Like Sky by Leslie Youngblood 

G-baby and her younger sister, Peaches, are still getting used to their “blended-up” family. They live with Mama and Frank out in the suburbs, and they haven’t seen their real daddy much since he married Millicent. G-baby misses her best friend back in Atlanta, and is crushed that her glamorous new stepsister, Tangie, wants nothing to do with her.

G-baby is so preoccupied with earning Tangie’s approval that she isn’t there for her own little sister when she needs her most. Peaches gets sick-really sick. Suddenly, Mama and Daddy are arguing like they did before the divorce, and even the doctors at the hospital don’t know how to help Peaches get better.