Keep your primary htaccess file as this:
Options +FollowSymlinks
RewriteEngine on
RewriteRule ^subsite/domain(/|$) - [L,NC]
RewriteCond %{http_host} ^domain\.com$ [NC]
RewriteRule ^(.*)$ http://www.%{http_host}/$1 [R=301,L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . index.php [L]
UPDATE:
And this should be your /subsite/domain/.htaccess
:
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /subsite/domain/
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . index.php [L]
</IfModule>