I appear to have made a couple hasty assumptions.
Let's back up. You need to hear your backing tracks (drums, other instruments, the song you are playing/singing/rapping/flatulating to), and you need to hear yourself. You also need to get the signals from mics and instruments into the computer to record. You, further, need to hear what you are playing, without creating an infinite loop, by feeding the playback into an input on your card.
The mic/line signals will go to the preamps or line inputs on the mixer. Personally, I would use the inserts to send your signal to the computer. Just put a regular 1/4 cable, one click only, into the insert jack of the channel you want to record, and the other end into the one of the M-Audio's analog ins. You will need an RCA adaptor at the card. Then, connect the outs on the card to one of the B inputs on the mixer, with an RCA to RCA stero cable.
The use of the inserts in this manner means the input signals leave the mixer, never to return on their own. The signal from your software, through the M-Audio analog outs, into the B input on the mixer, will be the only source sent to your 2.1's. If I read you properly, you have the speakers correctly plugged into the main outputs (labeled exactly that on the mixer) of the Peavey.
In any case, any mixing will now occur in the computer, you won't have any control over levels, EQ, panning or whatever on the Peavey. The output generated by your software will be what you hear. For recording, unplug or turn off or down the monitors, and use your headphones.
I think that'll work.