How do I send a message to stderr from cmd?

You can try redirecting the handle of STDOUT to the handle of STDERR. In your child process, perform the echo with a handle redirect:

:: Writes a message to stdout 
:: (which in the parent is piped to stdout.log)
echo message

:: Now I want to write a message to stderr 
:: (which in the parent is piped to stderr.log)
echo message 1>&2

Microsoft ‘splainin it