add_shortcode( 'scheduling', 'scheduling_shortcode' );

function scheduling_shortcode( $atts, $content = '' ) {

    $atts = shortcode_atts(
        array(
            'site' => null,
        ), $atts, 'scheduling' );

    $atts['site'] = do_shortcode( $atts['site'] );

    return // whatever it's supposed to look like
}