Remote Desktop – Access Host’s Smart Card Reader

It is not possible. When connecting remotely using RDP, Windows enables some remote smartcard services which disables local smartcards until RDP client supports smart card redirection (at least for most smart card readers). Windows Remote Desktop for Mac does not support this.

You might be successful using rdesktop which can make use of smartcards. You will find it in all major package managers like homebrew, macports and fink.

I've checked all third-party RDP clients I could find, none were supporting smart card redirection.

Only possibility: Only connect using VNC or other software - I am using Teamviewer for this purpose. Not sure about whether someone else may be connected using RDP at the same time you connect.

You need to disable Smartcard Credential Provider.

The easiest way is to use Autoruns tool from Sysinternals. In Winlogon tab disable mentioned provider (you may need to uncheck Hide Windows Entries in Options menu).

Alternatively you may just remove following registry key:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Authentication\Credential Providers\{8FD7E19C-3BF7-489B-A72C-846AB3678C96}

This worked for me on Windows 10, but it should work on Windows 8 too.