I'm not sure what you think you can get from this site, if you ignore our guidance as well as dictionary definitions.
It's not redundant. Tutors can teach small groups or provide 1:1 tutoring. A school may provide a tutor for someone who has to miss class due to illness - that's a public tutor, not a private one. Whether you consider "private" to mean individualized instruction or paid for by personal instead of public funds, you can have group tutors or public tutors, so the phrase is not redundant.
Perhaps you could take a look at using capital letters and proper punctuation.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.