"to your gates": From this I understand the gate (i.e., beth-din) in which they were judged. It is, therefore, written "your gates" (here) - "your gates" (Ibid. 2) for a gezeirah shavah (identity). Just as "your gates" there refers to the city in which they are found, and not to the beth-din in which they were judged, so, "your gates" here.
"that man": and not one who was forced, and not one who did so unwittingly, and not one who was under some kind of misapprehension.
"that woman": and not one who was forced, and not one who did so unwittingly, and not one who was under some kind of misapprehension.