What is going on when I can't access an SMB server share (not accessible error) until I run cmdkey to delete the credential?

It is possible that the local time and the machine hosting the shares are out of sync. Though your domain admin should be taking care of this. Typically when token for your credentials is passed to the machine but is out of sync, it will stop working.

Another possibility is that your local machine might be trying to pass your domain credentials to the Windows Home Server. And being it is not part of the domain, it would bounce you out.

Though admittedly, it shouldn't let you login in either case (unless the domain controller and your workstation are synced up, but the Windows Home Server is not).