If you can find a way to route discord's audio into a new virtual audio input device, it should be possible. There are a few virtual audio loopback device drivers out there, it might be tricky to set up though.
To run two instances of RahiTuber separately, i would suggest copying the program to a new folder. That way the copy can save its own config settings (like the most recent layer set, microphone, screen position etc).
The "name windows separately" option will also be necessary to keep your screen capture software from being confused.
Hope it works!