Create a Windows account on the member server that has the name username and password as in the domain (or corresponding local account on the SQL Server)
Specify the username and password in the connection string without using the doman or servername prefix.
That works with two servers that are both in a workgroup (IIS and SQL), so I suspect it should work.
Cheers
Ken
Microsoft MVP - Window Server (IIS)
MCITP (EA, SA), MCTS (ISA, SQL Server, Hyper-V, MOSS, Ops Manager), MCSE+Security, MCDBA