There is useful information that could be found in this article
It seems that the first site is a subdomain of the other site. Our suggestions is to go to the web.config file and find where we register this module:
You need to inherit it and register the new custom module in the web.config file. The system should use your custom module, not SitefinitySessionAuthenticationModule.
You should verride InitializeModule, then call base.InitializeModule(context) and set:
This will change the name of the cookie for Sitefinity, it will not be the default FedAuth and
it will not cause conflicts.
Do you want to have your say in the Sitefinity development roadmap? Do you want to know when a feature you requested is added or when a bug fixed? Explore the Telerik Public Issue Tracking
system and vote to affect the priority of the items