How do you plan on updating the Global Variables?
If you plan to do this when you move the package from one environment to the other, I would suggest you use an ActiveX script as your first step as follows:
Function Main()
DTSGlobalVariables("strDataSource").Value = "(local)"
DTSGlobalVariables("strUserID").Value = "user"
DTSGlobalVariables("strPassword").Value = "pwd"
Main = DTSTaskExecResult_Success
End Function
Next create a Dynamic properties task.
For the Data Source, double-click the DataSource of the connection. The Source = "Global Variable". Specify the strDataSource variable. Add the User ID and password the same way but at the OLE DB Properties level.
Good luck!