Hello,
It seems the Default Web Site is catching the requests for "test.mywebsite.com". You could stop or remove the Default Web Site to see if that resolves the issue, if the site is not needed.
Most likely the Default Web Site is configured to catch all unassigned requests.
It could be that "test.mywebsite.com" is resolving to an IP address configured in the Default Web Site's bindings and overriding the correct sites bindings.
Verify the DNS record for "test.mywebsite.com" matches the IP Bindings in IIS for the "test.mywebsite.com" site.
You could also configure the test site to make it accept all unassigned requests to see if that will work.
Hope this helps!
Brock Hensley
Technical Support Representative
http://www.ServerIntellect.comManaged Servers, 24x7 U.S. Support, Web Hosting Solutions.