Setting Up Training Domain

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I am trying to set up a training domain for a software product.
I have clientel that come into our office from various locations to get
trained up on the software that they have just purchased.

I am wanting to be able to have a connection string that the trainees
can come in and connect to the training server with our software
installed and work through our training materials.

I currently have a connection string like this:
DatabaseName_db=Integrated Security=SSPI;Persist Security
Info=False;Initial Catalog=DatabaseName;Data
Source=trainingserver\;User Id=sql1;password=xxxxx
to connect to the training server.

What needs to be modified to connect a computer from an independant
domain to this sql server?

.