It’s not my job to teach you the proper relationship between Jesus and the Word of God.
But you are wrong. New Testament Only Christianity misrepresents who Jesus is, and what the importance of the Jewish scriptures is.
You misunderstand both. The OT doesn’t teach corporal punishment for children. No shepherd beats his sheep. The “rod” is illustrative and figurative of the Word of God, not a physical tool for punishment.
Jesus Christ is the God of the OT and he’s consistent.