Hi,
Why do you want to have the two children folders do not share the session states ? If that is for security consideration, is it possible use authorization instead?
Below is article about paths to resources resolution, hope helps:
ASP.NET Web Site Paths
http://msdn.microsoft.com/en-us/library/ms178116.aspx
As this is an ASP.Net question rather than IIS. It is recommended you get further support at our ASP.Net forum. Then engineers and communities there can help you in a more efficient way.