What needs fixing if one of my rear wheels spins more than the other when trying to hook up? Someone told me once that my "rear clutch pack" needs replacing. Does any of this make sense?

Keep in mind it's got an IRS
01 cobra.

 

Yep. The "Traction Lok" limited slip differential in your Cobra has small clutches that are used to tie the side gears (and thus axles) to the carrier. If they wear out or the spring providing the preload for the clutches weakens, you'll start seeing "one wheel peels."

The Traction Lok doesn't have a particularly high torque bias so it's not hard to get one wheel spinning when, say, going around a corner on dry pavement. If you've got some serious power you might consider upgrading the diff while you're in there...

 

Most Mustangs do that when cornering or trying to do a donut on dry pavement, I wouldn't worrky about it unless you get "one wheel peel" in a straight line, in which case you will need new clutch packs or possibly add a shim to the existing ones.