President Zhang is their biological mother. Hong Shina is the first daughter of President Zhang. She may be an illegitimate child. Because she couldn't support herself, she gave it to Sister Yu Man and promised never to recognize her. Park geun-hye is park geun-hye's second daughter, born after President Zhang married park geun-hye's father.
In the plot, it is not clear why the nun does not want President Zhang to recognize her relatives. Personal guess may be for Hong Shinan, or it may be emotional reluctance. It is inevitable that Park Hao will treat her better than Hong Shinan.