Is it Halal to shave the hair of my and my wife's privat part too?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

A spouse can shave pubes of the other since looking and touching the private parts of spouse is permissible whether it is for enjoyment or any other purpose. It is reported in a sound Hadith that the Prophet (Sallallahu Alaihi wa Sallam) said: "Conceal your private parts except from your wife or your slave woman." [ Ahmad, Sheik al-Arnavoot graded it as good].
Allah knows best.