Would this help? This is a badly-edited engineering test I did with Denise.
We’re four time zones apart. Everything you hear is live and real-time at the time.
https://www.kozco.com/tech/audacity/clips/DenisePodcastVer5.mp3
You didn’t describe what the class was, and I’m sure there are going to be holes in it, but I can do some of it. This is a cousin to the way broadcasters do it.

The machine on the right runs Zoom. This one is running Skype. No option. You can’t share the machine with other jobs. Skype/Zoom won’t let you. They’re very firm about that.
The machine on the left plays sound clips and records the complete mixed show.
Those two older Macs have Stereo Line-In and Stereo Line-Out.

If you’re not blessed with older Macs, you may need USB adapters such as the Behringer UCA-202. Ignore the earphones in this illustration.

The mixer is a Peavey PV6. It does not have built-in effects, but it has the ability to send a separate signal to an effects generator and then bring it back in. That’s important.
You should be on headphones and listening to the mixer. Your microphone should be plugged into the mixer.
The headphone connection of the Zoom machine goes into the mixer just like any other sound source like a cassette machine or other music player.
The headphone connection of the left machine goes into a mixer input. So now the mixer can select between your live microphone, the left machine for music playback and the Zoom machine for audience comment and questions.
Still missing one pathway. The second, special output of the mixer goes to the Zoom machine audio in. In this case, it’s the effects-send service, not the mixer main output. Select all the sound sources of the mixer except the Zoom sound.
To recap. The main mixer signal has everybody in it and gets recorded on the left machine. The special output of the mixer has everything but the Zoom voices on it and goes back out to the Zoom audience. That prevents feedback, echoes, milk jug voices, and delays, but lets the audience hear high quality versions of everything you’re doing.
I know this is hard to follow. It’s like reading the three volume set “How to Ride a Bicycle.”
I actually generated signal pathway and schematic illustrations here somewhere.
The broadcasters call this process “Mix Minus.” Zoom gets everything minus their own sound. That’s what lets the news anchors carry on a conversation with the field reporter seamlessly except for possibly a delay here and there if they decided to use satellite.
Let me know if I should look for those diagrams. I don’t know what the modern version of that mixer is.
Note the machine on the left doesn’t have to be another computer. It can be a sound recorder capturing the main output of the mixer and a separate music player…or more than one. Depends on the capacity of the mixer.
Koz