MSTest unit test passes by itself, fails when other tests are run

I suspect the other tests are modifying some value in the DLLConfig class that is causing the result of the getter to change. Unit tests should always be run from a known initial state, so you should either set this up in the test method itself, or in a method marked with the TestInitialize attribute which is run before each test.

Your test is depending on an external file. Instead of calling a function that directly accesses the file you should have DLLConfig.Domain call a method in another class.

public static string Domain
{
    get
    {
        return _domain = AlwaysReadFromFile
            ? CredentialReader.Read(DOMAIN_TAG)
            : _domain ?? CredentialReader.Read(DOMAIN_TAG);
    }
}

Then you can initialize DllConfig with a mock/fake/stub CredentialReader where you can control its return value. Remember you are testing that DLLConfig.Domain is returning the correct value based on the AlwaysReadFromFile condition. You shouldn't be testing where that value is coming from (or if it even exists) at the same time.

Making your DLLConfig class more "testable" has the added benefit of separating out concerns. When you are thinking about a class and can't help but say "This class does this AND that" (abstracting configuration data and reading that data from a file) its a good bet the class is mixing concerns and trying to do to much. If DLLConfig is an abstraction of configuration data it should focus only on that and leave where the data comes from to another class.