From a leader of the empire standpoint, hiding the truth of the founder makes sense. If your origin story is less clear cut than people think (chosen by god, eliminated [genocide] the witches who were simply evil and definitely had no individuality whatsoever*) they may start to wonder why can't someone else lead.
At a minimum, I think she should continue to educate the ruling family so they can learn from the past/be aware that witches are coming for revenge. Even if it's not directly from the diary or she doesn't trust dad & bro with this info, it seems pertinent to tell at least one person as backup and ensure future generations of imperial family know what's up.
From an equity standpoint though (separate from the story as it exists), I would want that diary/the true history shared with the public. People should understand both the good and the bad of their history so they can make their own decisions and grow from it.
*This phrasing about the witches is my salt about non-dynamic, whole-species/race villains. Even in fantasy, writing an entire group of people (or humanoid fantasy species) is a dangerous dynamic. It allows readers/inhabitants of the world to hate that group or rejoice at their deaths, simply because they belong to that category. Plus, any person writing in the real world has inherent biases and that means such a group would usually end up with racist or other bad connotations (even if that's not your intention!)
So, anytime you read or write where an "entire group is evil, all of them, it just can't be helped" think a little harder. If you're writing it, maybe consider making them non-humanoid or brainstorm ways to make that group more dynamic/layered (you will have inherently richer world building for it!)
