I don't understand and wouldn't pay for the "stabilizer" - it's just a square made out of PVC. I'd try to figure out some sort of strap with stakes on each end (plus sandbags or whatever). The problem I've had a lot is that the dog runs in and just takes the whole thing with him, which the stabilizer (which I guess prevents rolling side-to-side) isn't going to help. Also make sure the actual fabric chute is attached really well to the barrel, otherwise the dog could pull it off of the barrel and get tangled.
I used to have a 2' piece of tunnel that had built-in places for stakes (you could also use a normal tunnel brace, that stakes down and then has places to bungee around the tunnel). And then the chute attached to that. Once I figured out how to rig it so the chute was really securely attached, it worked pretty well. I think it was from Ebay though so I don't know where you'd get something similar.
Be really careful. Neither of my dogs could care less about getting tangled in a chute or anything, but it's the last thing you need with a dog who's already having problems. If there's a nice solid chute at wherever you take class, you might want to ask about just coming early or staying late to work on it. It's convenient to have a helper anyways.