Wordpress htaccess redirect destroys my non-www to www redirect

In my root domain I have an .htaccess to redirect non-www to the www, and to redirect to a subdirectory (containing a temporary website). This is done using the following code:

Options +FollowSymLinks
RewriteEngine On

# non-www to www, exclude localhost
RewriteCond %{HTTP_HOST} \.
RewriteCond %{HTTP_HOST} !^www\.
RewriteRule ^(.*)$ http://www.%{HTTP_HOST}/$1 [R=301,L]

# temp redir to subdir-wordpress
RewriteRule ^$ /subdir [L]

In the subdirectory runs a Wordpress setup using the following .htaccess:

# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /subdir/
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /subdir/index.php [L]
</IfModule>
# END WordPress

What happens is that people get redirected to http://domain.com/subdir, while I want them to end up at http://www.domain.com/subdir. I tested with curl and noticed that it redirects with these steps:

1. domain.com => www.domain.com
2. www.domain.com => www.domain.com/subdir
3. www.domain.com/subdir => domain.com/subdir

So the .htaccess in the root dir seems to work fine. But the automated Wordpress .htaccess seems to destroy my hard work :-)

Anyone knows how I can modify the Wordpress .htaccess so it does work?