SQL Server instances, to multiple domains

Hello Experts.  I hope you find this thought-provoking

My desired scenario- two servers, each a controller for its own domain.  Users will connect via Terminal Services to each.  A third server will run SQL Server.  

My first-choice outcome- The SQL Server would run two instances, each containing the databases for one of the domains.  A given domain would see only their instance, and thus, their own databases.  

My second-choice outcome- The SQL Server would be visible to each domain.  I could then configure their application software to point to the databases in their instance only.  
Michael HaleAsked:
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NJComputerNetworksCommented:
you can configure either choice...

SQL supports local database security (created user names and passwords per database)  or integrated security ---using domain based ID's for secure access to the database.

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Microsoft SQL Server 2005

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