Even though I have such a bad time explaining my ideas and points, I am going to try anyway
First. Vermouth followed what she thought was Araide car. She was fooled by the FBI at that time. In a way Araide and family were placed in protective custody. If I am reading this right, then they must have accepted FBI's protection. In order to get that, the FBI would need to explain why they needed to be protected. The FBI is not allowed to put people in protective unless those people accept it. It can not be forced on them. A normal person is going to ask questions and need to be convinced why such action is necessary. Thus, I find it hard to believe like you suggest that Araide and family do not know part about what is going on. After all they allowed themselves to be put in Protective Custody. Read this link
Question from a writer
&Partsu Chapter 459 Page 17 Jodie is talking to Araide and says this "that you're working naturally at school without being suspected by anyone" His reply "Yes, it's all thanks to you...
because you told me in detail how the person disguised as me acted at school"
What I meant was in order to make it appear like the real Araide did not appear strange, he needed to act just like the Vermouth Araide, otherwise, the student might have started to wonder what happened to change the Araide they knew. Jodie explained how the Fake Araide acted so the Real Araide could act that way
To use your words Araide knows how to impersonate vermouth
's Araide
Does that explain it?