Is it permissible to inform the mother or the social supervisor about a teacher who is not fully performing her duties at school, and is that considered backbiting?

If the teacher is remiss in her work and responsibilities, there is no harm in informing whoever can rectify her and deter her from her shortcomings that harm the students. This is not considered forbidden backbiting, because it is permissible for the oppressed to complain to someone who has the ability to remove the oppression, or to seek help from someone who can change the evil. The reporting must be for the purpose of changing the evil and redressing the injustice, not for revenge.