Ah well a Workgroup and a Domain are very different. In a Workgroup its going to be hard to get this to work, because each computer only knows about the accounts that exist locally on itself... So when you try to access something on a remote computer you will only be allowed to access it if whatever resource you are trying to access (a file or directory for example) has been set to allow Everyone access. Everyone is a built in security group that literally means absolutely anyone - very unsecure but often the only choice you have in a Workgroup. The only other way you can get access to something on a remote machine in a workgroup is if you supply the username and password of a local account on the remote machine, however the IO.Directory.CreateDirectory method does not have an option to provide credentials.
I was going to suggest calling the Net.exe command line program that is built into Windows and using that to create a connection to the remote file system (as it has the option to supply credentials to be used) but I just tested it out against an XP machine in a workgroup and cant get it to work, it just keeps saying the password is incorrect even when I know it is not. So... I'm afraid I haven't really got any other suggestions and would have to say that I think what you want to do is not really possible in a workgroup. Hope someone else can be of more help!