Issue is that pretty much all the information for any automation tool isnt available over RDP (or VNC) as interacting and reading application state typically requires some form of introspecting into SUT. Afaik, Sikuli does not have this limitation so it could be an option… Last one, but still an option.
If you have access on the box you RDP into, you could use remote libraries via: GitHub - robotframework/PythonRemoteServer: Robot Framework remote server implemented with Python
Process is something like this: run remote server on the box you rdp into, install the required libraries and tweak what is needed on the host you are running robot.