I've been trying to do a similar thing to you - logging performance data to SQL for two separate machines, which were not part of a domain and have come to the same conclusion that you're unable to use SQL Server Authentication.
Was just wondering if you had come across a workaround in the meantime?
Sorry I didnot update this post after I resolved the issue
- I added entry for remote domain machine in hosts file (C:\WINDOWS\system32\drivers\etc\hosts)
- then created a windows account in both the machin with same UID + Password (as local administrator)
- created SystemDSN for this connection
Edit: - and run Perfom under this account
This worked for me