WordPress – Wrong urls at wp-admin at wordpress with subdirectory and proxy

I am using apache2 and mod-proxy to integrate wordpress blogs into subdirectories of my TLD.

• Main site: example.com
• Blog1: [http://example.com/blog]
• Blog2: [http://example.com/other-blog]

Apach2 virtual host of the main site with proxy:

<VirtualHost *:80>
ServerName example.com

...

# Rewrite rule to add missing slashes
RewriteRule ^/blog$ /blog/ [R=301]
RewriteRule ^/other-blog$ /other-blog/ [R=301]

<Proxy *>
Order deny,allow
Allow from all
</Proxy>

ProxyRequests off
ProxyPass /blog/ http://blog1.localhost/
ProxyPassReverse /blog/ http://blog1.localhost/
ProxyPass /other-blog/ http://blog2.localhost/
ProxyPassReverse /other-blog/ http://blog2.localhost/

...

</VirtualHost>

Apach2 virtual hosts for blogs:

<VirtualHost *:80>
ServerName blog1.localhost
DocumentRoot /var/www/blog1/
<Directory />
Options FollowSymLinks
AllowOverride All
</Directory>
</VirtualHost>

Linux hosts file add lines:

127.0.0.1     blog1.localhost localhost.localdomain
127.0.0.1     blog2.localhost localhost.localdomain

WordPress: Settings > General Settings:

• WordPress address (URL): [http://example.com/blog]
• Site address (URL): [http://example.com/blog]

The .htaccess file:

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

This setup works fine in general. Unfortunately the back end of WordPress has problems at some parts by stripping the sub-folders in URLs resulting in problems of saving settings or loading pictures. eg.:

• Uses: [http://example.com/wp-admin/…]
• Should use: [http://example.com/blog/wp-admin/…]

or

• Uses: [http://example.com/wp-content/…]
• Should use: [http://example.com/blog/wp-content/…]

What I tried so far:

• used various rewrite rules suggested
• used various modifications in wp-config.php found here: http://codex.wordpress.org/Editing_wp-config.php#WordPress_address_.28URL.29 *
• searched the mySQL database for wrong set URLs

Nothing of it worked so far or made it worse.

If somebody has an idea of how to solve this problem I would very much appreciate this.

*) Edit: What I already tried here:

define('WP_HOME',  'http://' . $_SERVER['HTTP_HOST'] . '/blog');
define('WP_HOME', 'http://example.com/blog');
define('WP_SITEURL', 'http://example.com' . $_SERVER['SERVER_NAME'] . '/blog');
define('WP_SITEURL', 'http://' . $_SERVER['SERVER_NAME'] . '/blog');
define('WP_SITEURL', 'http://example.com/blog/');