Can you use different domain user in your Spotlight on Windows connection instead of Diagnostic server service user, from Diagnostic server machine to the monitored machine ?
Can Spotlight on Windows connection monitor O/S in different domain ? yes, in general.
The longer answer is that it depends on the trust between the domains. The easy way to work it out is whether you can connect to any shared resources in the other domain using your account.
Or even more simply create a share on the box you want to monitor. Try and add the user you want to enter as the user in Spotlight as being allowed to access the share. It will complain if you don’t have trust set up right.