How to point URL path to a wordpress folder - wordpress

Question

I currently have two sites, hosted on the same server using Apache virtual hosts.
http://www.example.com -> /var/www/sites/mysite (path to main website)
http://blog.example.com -> /var/www/sites/blog (path to wordpress folder)
I need my blog to be accessible from www.example.com/blog
I cannot move the wordpress installation into a 'blog' subdirectory of the mysite folder.
Using the Apache Alias directive, I can do the following in the configuration for www.example.com:
Alias /blog /var/www/sites/blog
and access the blog via www.example.com/blog
However the following fails to work with a 404
www.example.com/blog/a-permalink-post-title
I have also tried using the following but the 404 still persists.
AliasMatch /blog/(.*)$ /var/www/sites/blog/$1
The current virtual host configuration looks like this:
<VirtualHost *:80>
ServerName www.example.com
Alias /blog /var/www/sites/blog
DocumentRoot /var/www/sites/mysite
<Directory /var/www/sites/mysite>
Options Indexes FollowSymLinks
AllowOverride All
Order allow,deny
allow from all
</Directory>
</VirtualHost>
and for blog.example.com
<VirtualHost *:80>
ServerName blog.example.com
DocumentRoot /var/www/sites/blog
<Directory /var/www/sites/blog>
Options Indexes FollowSymLinks
AllowOverride All
Order allow,deny
allow from all
</Directory>
</VirtualHost>
Would greatly appreciate any help with this.