How to Configure TSWEB 2008 to allow access to local workstations?

I need assistance with configuring my Windows 2008 Terminal server to allow RDP access to other computers on the local domain from the Internet.  I would turn the TSWEB into an RDP portal.

TSWEB is installed and working. I can connect to the TSs desktop from the Internet using TSWEB along with remote apps which I am not using.
 
When I access TSWEB and choose the Remote Desktop option on the web page, I am given the option to connect to another computer. If enter the name of a computer on the same network the terminal server resides, I am rejected. The system states it cant find computer xyz and try again
.
From what I can understand, is that TSWEB is trying to resolve computer xyz using an Internet DNS and sense the computer name doesnt exist, it is denied.

First, is it possible to do what I ask? To allow RDP access to domain computers through the terminal server?

Second, IF so, how do I configure TS to look inward to resolve these host names?

Thanks