Henrik Juel ,
I guest the problem is that your root app and the sub app use the same key for ASP.NET Forms authentication.
in web.config , you can see something like :
<authentication mode="Forms">
<forms name="YourFormsAuthName" />
</authentication>
If your root site and sub site use same name , the sub site will get error because the root site send your sub site the invalid cookie.
So , please modify the sub site , and use another name.
--
If you want to keep the same name ,
you need specify the machineKey for both site.
Regards,
Terry