Hi,
Thank you for posting in our forum.
In general, all domain trusts in a Windows Server 2003 forest are two-way, transitive trusts. When a new child domain is created, a two-way, transitive trust is automatically created between the new child domain and the parent domain.
In a two-way trust (Transitive), both domains that are involved in a trust relationship trust each other.This means that authentication requests can be passed between the two domains in both directions.Some two-way relationships can be non-transitive or transitive depending on the type of trust being created.
As a solution to configure the different authentication types for different trust ways, we could change the authentication type to Selective Authentication on both of the domain trust way. And then we could try to grant the different Allowed to Authenticate permission for different trust ways to achieve your target.
For detailed information about authentication types, I suggest we could refer to the following article.
Configuring Selective Authentication Settings
http://technet.microsoft.com/en-us/library/cc755844(v=ws.10)
Additionally, please refer to the article below to secure trust.
Security Considerations for Trusts
http://technet.microsoft.com/en-us/library/1f33e9a1-c3c5-431c-a5cc-c3c2bd579ff1
Regards,
Vicky