I keep running into this same problem, and I never find a solution other than just creating a separate website.
I always get errors when creating an asp.net virtual directory inside of another asp.net site. I have found many blogs with work around to remove things like http modules and I belive another about surrounding the system.web portion with <location> with a parameter of something like donotinheritparent=true.
None of the things I have found work, I try and try but never get the sub app to run. Of course every time I have tried this, they have been completely different apps, occasionally targeting different frameworks.
Would I be right to say that this can’t be done, if we assume that the child config cannot inherit anything from the parent to work?