Hmm, ok. Aside from user authentication, you may run into another problem here. WinRM usually requires the remote computer to also be authenticated, and it uses Kerberos to accomplish this. Without any trusts between the domains, that would also fail.
If you need to use PS Remoting in an environment where the computers can't use Kerberos authentication with each other, you need to do one of two things: Either set up an HTTPS listener (which provides a different sort of computer authentication), or use the TrustedHosts list on the client computer (which is less secure; you might be connecting to a rogue server.) There is information on both of these approaches in the free "Secrets of PowerShell Remoting" eBook which you can get from this site, by clicking Resources and then Free eBooks along the top ribbon.