Global login and domain mapping compatible?

I have 100 root domains and then thousands of subdomains. All of them are accessible to all logged in users. I need global login, so user only logs in once. Global login works, however, not when I domain map. Or domain mapping works, however, not when I have global login.

All of my mapping is done only by the Admin, never the end user. The mapping is simple. I go into Admin --> Sites, and create a subdomain off the install domain. Then I map this to the other root domains in the network. Example:

rootdomain2.installdomain.com --> rootdomain2.com.
rootdomain3.installdomain.com --> rootdomain3.com.

Would greatly appreciate your help!!