I am really confused here also. If you are using a servlet to redirect, why are you using ajax to make the call for authentication? When not just do it in the servlet since it has to perform the redirect anyway?
my user's application servlet searches in my authentication server's domain.
Your user's application servlet? Is this servlet number 1 or servlet number 2? Please explain. You user doesn't own the servlet, right? Also, what is it searching for in the authentication server's domain?
how to get the html object look for the user's application servletcontext
What html object are you referring to here?