Don't waste your time, we have tried popen many months ago. It is fine for Linux, but it won't do for Windows.
Stop does work. Within the operating system's capabilities.
Your objection regarding wxKill is correct, but that is a known Windows problem. Windows does not support any such thing as SIGTERM (which would be the right thing to use in this place). The only alternative would be to use SIGKILL, that would certainly end the process, but this is not an option, for obvious reasons.
Under Linux, the stop button works as you expect it, because SIGTERM is used.