Assessing admin when site is not hosted in the root of the domain We set up a site with a url like www.mysite.com
the site is being served by a proxy to come up as 

www.theirsite.com/mysite/

We set $base_url  to www.theirsite/mysite

This is working correctly to load all the assets on the page but does not work on the admin.

The admin login and all pages on the admin try to post to the root of www.theirsite.com
so for instance the /user page tries to post to
www.theirsite.com/user
this is obviously not working.

We tried clearing the cache on drupal to rebuild all urls as was recommended on many sites, but did not have any effect.

We are hosting our site via iis7 on windows.
The version of Drupal is 7.2

What can be done to fix the admin form urls?
Our solution was to create a virtual folder mysite and host the site as
www.mysite.com/mysite

After that the proxy was pointed to the new virtual folder.  This made the admin work correctly. 

This is not a satisfying answer as it still leaves unanswered how to control the admin form urls