Configure two separate websites having one as a child of another

Create two sites and one application on the first site using the WebAdministration Powershell Module.

New-WebSite -Name Site1 -port 80 -HostHeader www.site1.com  -PhysicalPath "C:\inetpub\Site1"
New-WebSite -Name Site2 -port 80 -HostHeader www.site2.com  -PhysicalPath "C:\inetpub\Site2"
New-WebApplication -Name site2 -Site Site1 -PhysicalPath "C:\inetpub\Site2"  

Site2 is then accessible via www.site1.com/site2 and www.site2.com

The key is to point the second site and the application to the same physical path.