I don't have a polished solution for you.
But I can help get the ball rolling a bit.
Basically you need the computer to send audio from 2 applications, to two different destinations.
Without a specialized 3rd party application, which may exist, but I'm not aware of, you need one of the two applications to give you a preference setting to choose output direction ased off of what the computer can detect and what you have setup in your "Audio MIDI Setup" (Utilities folder) application.
This places the problem onto the applications you are trying to use.
Plex doesn't have such a choice I believe.
However VLC does. I use VLC when experimenting with surround sound files.
Which I send to 3 stereo USB dongles that act together to send the audio to 3 pairs of stereo speakers (or the equivalent). This is done by setting up a profile for those dongles in "Audio MIDI Setup"
Anyway.
Quick answer:
VLC unlike other applications can choose an audio destination other then the system default.
1. If she is using Plex, you aim the main system sound through the HDMi cable, and play your music in VLC while aiming VLC at the USB device.
(Use VLCs Playlist window to queue up your music)
2. If she is using VLC, aim VLC towards the HDMI, and set the system audio to the USB device while you use iTunes.
Not perfect, still requires some thought and preparation.
But it is free!