Is there any way to send two different audio sources through the main audio outs and the headphone out on a UR-22C?
Short answer is sadly NO for the UR22, but YES for the UR44.
If you don’t have the UR44(C), a possible workaround could be to route your 2nd audio to your laptop’s audio jack. You won’t have the same quality audio of course, but it could be good enough. You’ll need to know well your DAW’s configuration menus to use both the UR and the latop’s jack (and generic ASIO) at the same time, but it might be doable on your setup.