>>>I am wondering if the following steps are "normal" when trying to execute a SP when connected to SQL Server 2008 on customer site (the reason I put "normal" in quotation marks is I don't experience this when using SSMS on local copy of SQL Server).
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>>>I connect to their SQL Server (via VPN and SQL Server Authentication). Then I want to attach a database so I open New Query window. As soon as I open it and start typing, I get the Connect window (I have not even clicked on Execute yet). But entering my user name and password in this Connect window does not work. That is, I get a rejection message. I am surprised that I even get this "second" Connect window when opening a new query window. Is this the way it should work?
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>>Is your computer on the same windows domain as the SQL server (I bet it isn't)?
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>No. You won the bet <g>
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>>If not (even though you may authenticate to their VPN), you may need to run your SSMS as a user on the domain the SQL server is on.
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>>From a command window you would execute..
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>>"RUNAS /user:myDomainB\theirusername /netonly "C:\Program Files\Microsoft SQL Server\100\Tools\Binn\VSShell\Common7\IDE\Ssms.exe""
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>>..Substituting their windows domain name for myDomainB, their windows domain username for theirusername (you'll be asked for the password), and using the correct path to SSMS.EXE.
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>I don't quite understand what to use for myDomainB. They (the customer) only gave me a user name and password to SQL Server. Should I ask them for their "domain name"?
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>Thank you.

Very politely ask them for a valid windows user name and password on their domain. It doesn't have to have administrative rights (you'll get rights in SSMS when you connect to their database). They can tell you their domain name.

I've had this issue before by the way. Not exactly the same symptoms, but SSMS has problems functioning across domains.