In the novel, Adri is Linh Cinder's step-mother, while Pearl and Peony are Linh Cinder's step-sisters.
As for Linh-jie, this is a reference to Adri in the second chapter of the book. In this chapter, when Cinder returns to her apartment, she sees her step-sisters, Peony and Pearl, clothed in beautiful gowns. Meanwhile, a seamstress is fiddling with the neckline on Peony's gown. Linh Adri, Peony's mother, has just given the seamstress the order to lower Peony's neckline. Adri also orders the seamstress to take in Pearl's dress at the waist. When the seamstress objects, stating that the gown is already too tight and that it would be very difficult to dance in it, Adri ominously proclaims that the purpose of the dress is to find Pearl a husband.
In response, the seamstress mentions that, at seventeen, Pearl is too young to get married. However, Adri coldly answers that she expects results from the gown, meaning that she expects the dress to earn Pearl a husband. Obsequiously, the seamstress assures Linh-jie (Linh Adri) that Pearl will be as beautiful as the morning dew, when she's finished with her dress. So, Linh-jie is just a respectful way for the seamstress to address Linh Adri.