The default directory for Apache is set using the DocumentRoot directive. By default xampp apache uses "/xampp/htdocs" and uses default.php to then redirect requests for
http://localhost to
http://localhost/xampp.
Changing your DocumentRoot in httpd.conf to "/xampp/htdocs/mywebsite" will give you what you want but will have the side effect of making your xampp admin site inaccessible. An alternative would be to setup virtual hosts where the xampp admin site would be accessible only from the local machine, and all others available from outside the machine.