/*
Plugin Name: Redirect Main Site To Sub-Site
Description: Redirect 'main-site' to 'main-site/sub-site/'
Version: 0.1
Author: WPSE
Author URI: http://wordpress.stackexchange.com
License: GPL2
*/

add_action('parse_request', 'redirect_to_sub_site');
function redirect_to_sub_site(){
    global $wp;

    #Sniff requests for a specific slug
    if('main-site' === $wp->request){

        #The URL to redirect TO
        $url = 'http://www.example.com/main-site/sub-site/';

        #Let WordPress handle the redirect - the second parameter is obviously the status
        wp_redirect($url, 301);

        #It's important to exit, otherwise wp_redirect won't work properly
        exit;
    }
}

#Sniff requests for a specific slug
if('main-site' === $wp->request){

    #The URL to redirect TO
    $url = 'http://www.example.com/main-site/sub-site/';

    #Let WordPress handle the redirect - the second parameter is obviously the status
    wp_redirect($url, 301);

    #It's important to exit, otherwise wp_redirect won't work properly
    exit;
}