My main public_html directory has the following .htaccess rules:
Options +FollowSymLinks
IndexIgnore */*
RewriteEngine on
# i
Change your .htaccess with this:
Options +FollowSymLinks
RewriteEngine on
RewriteBase /
# if a directory or a file exists, use it directly
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
# if request is not for the /sub-dir/
RewriteCond %{REQUEST_URI} !^/sub-dir/ [NC]
# otherwise forward it to index.php
RewriteRule . index.php