Nefunguje ti to, protože jsi dal child_info do group by a navic to mas i ve Where, takze prazdne tridy tam nebudou
Navazovat to pres class_name je taky hloupe, ale budiz.
Pokud pouzivas Left join, nemuzes to pak omezovat podminkami na konci, protoze ty ti eliminuji prazdne tridy, ale musis dat podminky do napojeni tabulek

Zkus neco takoveho (pripadne chyby si oprav)

Select *, school_class.class_name skola_trida 
  FROM school_class 
  LEFT JOIN child_info ON school_class.id_school = child_info.id_school_class and school_class.class_name = child_info.class_name
  WHERE id_school = 100 AND school_class.platne = 1
  ORDER BY school_class.id