I would like to redirect the default website on IIS to the Change Auditor Web-Client application (4344501)

First, you should make sure that the "HTTP Redirection" module is installed on your server.  You can find it listed in the Add Roles and Features Wizard on the Roles page under the Webserver IIS | Web Server | Common HTTP Features section.

1. Open IIS Manager from Start | Administrative Tools | Internet Information Services (IIS) Manager
2. Expand the server name in the connection pane, then expand the Sites and navigate to the domain. Double-click on Http Redirect option.
3. Mark the check box Redirect requests to this destination and mention the URL to which you want to redirect your site.
4. Set the redirect URL to be: http://<server_name>/ChangeAuditor
5. Turn on the checkbox for the "Only redirect requests to content in this directory (not subdirectories)" option.
6. Click on apply
7. Restart your web services to ensure that the settings are applied then you should be able to test to see if the redirect is working by opening your web browser and navigating to http://<server_name>