I'm using the webservice search function in Sharepoint, by calling the
QueryEx function from within my webpage.
In my Sharepoint portal I have two different sites.
The first one is my own so only I am added to the userlist of that
site. To the second site I have added a couple of other users to the
user list as Content Managers.

When these users logon to my website and search, they do not find any
of the documents in my first site but if they search on the name of
that site they get a hit and if they click on the result they get to
my first site and can then reach my documents anyway.
What can I do to restrict these users from using my site?

(I set the credentials of the searchfunction to
System.Net.CredentialCache.DefaultCredentials so the useraccount
should be used during search)