If you're using mIRC without a DLL, I just put a hidden DEFAULT button that when "pressed" will do what you want to happen when ENTER is pressed. Because ENTER works like pressing the selected button, this works fairly well.
Otherwise, I've had luck using KEYUP with key# 13 on DCX for handling the enter key.
That wouldn't work per the request, as the request stated that the information was to be sent upon the Enter/Return key being pressed.
Using the edit event, per your code, would have the information displayed in 3 being changed simultaneously with the information being changed in 4. The edit event doesn't wait for the Enter/Return key to be pressed before the rest of the event is completed, but completes all of the commands for every keystroke in the edit ID.