1) Does the school have a right to kick out the child. Yes. It's a private school.
2) Should the school kick out the child. I don't think they should. I think that keeping the child in school will help make a great witness to the mother, and hopefully the mother will decided to change her lifestyle. If there really is a problem with the child, then that is another story. I wouldn't want a child with bad language or behavior around the other 5 year olds.
Hmmmm, you mean do the Christian thing...