It is the "parents" of this child who are causing harm to her by openly living in a continuous state of mortal sin, thereby contradicting the Faith and morals of the Church - and teaching the child as she grows to do the same. Under these circumstances, the school would have little hope in helping the child "overcome that".
Education of any child is first and foremost the responsibility of parents who head the family. Any school, public or private, should be seen as ancillary to the family. A Catholic education is supposed to be just that. It is meant to teach not only reading, writing, math, etc., but to help instill the Faith and morals and example of virtuous living according to the decrees of God. In a word: Holiness. The eternal salvation of souls is paramount.
The disciplinary stand that the Church takes with parents of children as in this case, is meant to call them back to the fullness of Truth through conversion and repentance. The choice is theirs. The Church can't force them to accept it. For the sake of their souls, and that of their child, the Church can only hope that they turn from pride to penance.
Believe it or not, that held sway until Dewey.
You're about 80 years behind the revoltin' developments in Public Screwels.