SQL Server Windows Auth Login sees Domain as untrusted

a. Check that the user account the SQL Server service is running as a domain account.
From MSDN:

If the service must interact with network services, access domain resources like file shares or if it uses linked server connections to other computers running SQL Server, you might use a minimally-privileged domain account. Many server-to-server activities can be performed only with a domain user account. This account should be pre-created by domain administration in your environment.

b. Ensure the DNS server being used by the member server knows about the domain, i.e. can resolve SRV records for AD services. See this blog post for more information.

c. Follow resolution steps in the MS KB article.