Accessing C$ over LAN on Win2008R2 – cannot by hostname but can by IP and FQDN

1. If you are seeing SID's in local groups then your DNS or AD access is messed up from that server to either sub or parent domain IMO. RDP access could be a red herring and the real issue is proper connectivity to AD. Do you have event log events talking about unable to resolve account, etc? In a healthy server you should never see SID's IMO (unless accounts are deleted).
2. It's possible a GPO is affecting member servers security policy "allow log on through Remote Desktop Services" or the often forgotten "deny log on through Remote Desktop Services" inside the computer GPO config. You might be left out of the first or added to the second for member servers GPO, then that could be overwritten at the DC container level by the "default domain controllers policy". Run a Group Policy Results on a member server as you and see what shows up for:

computer config > Policies > Windows Settings > Security Settings > Local Policies > User Rights Assignments > two settings in quotes above

Not familiar with WMI Explorer, but does it let you specify the ImpersonationLevel?

Try the folling VBScript (not tested) on the local machine. Then edit the strComputer = "." line to be the server name and execute remotely:

On Error Resume Next

Dim strComputer
Dim objWMIService
Dim colClusterNodes
Dim objClusterNode

strComputer = "."

Set objWMIService = GetObject("winmgmts:{impersonationLevel=impersonate,authenticationLevel=pktPrivacy}!\\" & strComputer & "\root\mscluster")
If Err.Number <> 0 Then
    WScript.Echo "ERROR : Failed to get WMI handle [" & Err.Description & "]"
    Err.Clear
Else

    Set colClusterNodes = objWMIService.ExecQuery( "Select * from MSCluster_Node")
    If Err.Number <> 0 Then
        WScript.Echo "ERROR : Failed to execute WMI query [" & Err.Description & "]"
        Err.Clear
    Else 

        For Each objClusterNode in colClusterNodes
            Wscript.Echo "Caption : " & objClusterNode.Caption
            Wscript.Echo "State   : " & objClusterNode.State
            Wscript.Echo "Status  : " & objClusterNode.Status
            WScript.Echo ""
    Next

        Set colClusterNodes = Nothing
    End If

    Set objWMIService = Nothing
End If