The phrase “sought to put them away privily” is borrowed from Matthew 1:19, where Joseph, thinking of Mary, “was minded to put her away privily.” In Matthew, the phrase indicates Joseph’s desire to keep Mary from public humiliation, which is the exact opposite of what the people of Ammonihah desire. The phrase used in translation does not correctly demonstrate the intent of the people in Ammonihah. For them, they desired to put Alma and Amulek away very publicly.
Therefore, they were bound with strong cords and taken to the chief judge of Ammonihah. This would have been a very public binding, and it was probably better to say that they were paraded before the chief judge of Ammonihah, rather than simply taken. When they are there, the “people” witness against them. This was a very public event.
As Mormon lists the reasons that Alma and Amulek should be judged guilty of contradicting the laws of Ammonihah, they related the important theological difference about the Son of God living among the people, but not saving them. This, of course, was true, and was the very point of Alma and Amulek’s discourses.