So, the printer is normally physically connected to PC1 via USB or other cable. The printer is shared on PC1 to be accessable to other computer. PC2 is able to print to it. Now are you saying that when you move the printer to PC3, and you connect to a server via TS/RDP you are not able to print from the server to the printer?
This sounds like printer re-direct is not enabled on your RDP connection. When you first open Remote Desktop Connection to connect, click on the Local Resources tab, and then look at the bottom and make sure that the checkbox next to Printers is checked. If not, your computer will not make the printer available to the server. However, once connected to the server, you can add the printer as a network printer as long as it is shared on PC3.