Hi, I just encountered a similar problem. If I understand your problem, you want your edge child to have its own responsive.css, right? If that’s what you’re looking for, then first under your Edge Theme Options in wordpress, turn off responsive. This will prevent the parent responsive.css from autoloading. Then in your child’s functions.php put:
function edge_enqueue_styles() {
wp_enqueue_style( 'parent-theme', trailingslashit( get_template_directory_uri() ).'style.css');
wp_enqueue_style('edge-responsive', get_template_directory_uri().'/css/responsive.css');
}