Local host cross authentication

Local host cross authentication

I have two environments namely TedDev and TedLive (but it is the same
project) in my IIS and both sites have their own database and also their
own WindowService. Now when I test both sites simultaneously I get cross
authentication. Both sites are locally and are in their own app pool in
the IIS.
I don't want to create sub domains for each site. They will be deployed on
1 server so the issue will remain the same.
What I want to know what will be the best way to handle this, create own
authentication cookie or to configure the web.config files for both sites?
Any help would be much appreciated