The 1204USB mixer only sends the main mix outputs to the USB, and Audacity only records two channels.

When recording with Audacity, do you have the 1024USB selected as your recording device (Edit -> Preferences -> Devices)?

When you say "Everything sounds ok in our headphones", where have you got the headphones plugged in?

I think you are having issues with gain staging? While your XLR microphones are going into the mixer, send 1 should take XLR microphones to feed the telephone hybrid on send 1. Sound effects from your iPod/iPhone should be plugged into line inputs on your mixer and also sent to send 1. You need to treat the telephone hybrid almost like it is a external effects device i.e. digital reverb. The return from the telephone hybrid would go into line inputs 5 & 6. But the telephone hybrid should not be sent to send 1. Send 1 is set up for what we call a " mix minus ". Therefore the only thing you want to send on send 1 is the mix of the two microphones and the playback of your sound effects device " minus " the output from the telephone hybrid.

The master output level of the mixer and its internal analog to digital USB converter to the computer will only record the total mix coming from the discrete stereo bus of the mixer output left & right and at whatever level you are feeding out of the left & right stereo bus. If your record levels are low in Audacity, it is a function of the stereo output bus level of the mixer. The hybrid creates its own mix minus so that your microphones being sent via send 1 to the telephone hybrid are not returned at its output back into your mixer line level inputs on 5 & 6 and on five and six you are not sending that to send 1. This is also because there are various phase cancellation tricks going on inside the telephone hybrid. So you don't want the microphones and sound effects going to the output of the telephone hybrid. Where phase in fact may be causing a type of negative feedback phase inverted signal to cancel out your XLR microphones, sound effects and telephone caller from being recorded at an appropriate level. So you only want the caller's output to return to your mixer from the telephone hybrid. Again, the telephone hybrid output to your mixer should not include your XLR microphones nor sound effects back into the mixer. It should only be outputting the caller.

In turn, you should be monitoring the left & right output bus on the mixer and not send 1. Since the left and right output bus should include a mix of the XLR microphones, sound effects device and telephone caller. Some of the low recording issues could also be due to the computers operating system Microsoft mixer. The Microsoft mixer can be opened in its first default as simply a playback monitor mixer. But if you observe that, you should try the drop down menu to access the Microsoft mixer input recording controls. You can actually have 2 instances of the Microsoft mixer open simultaneously. One that displays your playback monitoring sources and one that displays your recording sources/input sources to be recorded. And that's how I've done it since 1978. And when all we had was analog equipment. But the signal routing remains the same along with the gain staging. So some of the problem may have to do with your actual mix output levels that are being digitized to record in the computer. And some telephone hybrid have different types of functions that output a mixed signal of everything. This mixed signal may in fact be phase inverted in comparison to the incoming source. So that makes when fed back to the mixer and included in the left & right outputs would actually be reducing the record level from 180° phase cancellation of a possible phase inverted output. So on the telephone hybrid you would not want the entire mix being sent out from its output that returns to your mixer. And that's where I believe your problem may lie?

I've custom-built telephone hybrids
Mx. Remy Ann David