I do have the dsn set up on both machines, but in further digging, I found this:

FIX: SQL Server ODBC Driver Ignores Authentication Setting (Q279526)

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The information in this article applies to:


Microsoft ODBC Driver for SQL Server, version 3.6
Microsoft SQL Server 2000 (all editions)
Microsoft Data Access Components version 2.6


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SYMPTOMS
When you use the SQL Server ODBC driver version 2000.080.0194, which was released with SQL Server 2000 and Microsoft Data Access Components (MDAC) 2.6 RTM, the authentication settings for ODBC data source names (DSNs) are ignored. The driver attempts to log directly into SQL Server using NTLM authentication (integrated security) without prompting for a user ID and password.

This can cause authentication failures, messages that database objects are not available, or unintentional modification of the wrong objects when copies of objects are maintained in multiple databases.



RESOLUTION
To resolve this problem, obtain the latest service pack for Microsoft Data Access Components 2.6. For additional information, please see the following article in the Microsoft Knowledge Base: