Well after sitting around for a couple days with only one person able to use the wheel I called Nintendo's support.
I'd messed around with the remote a bunch to no avail: Tried resetting it, playing with the remote/nunchuk (worked find) and trying the wheel over and over a few times.
When I talked to the man on support he was confused as well that it would work fine without the wheel but not in the wheel. He said it was likely the motion sensor had been dislodged and recommended that I slap the remote on my other hand to hopefully re-align it. I did once, not too hard really, then he had me put in tennis, which worked fine. He had me go back to Mario Kart and the darn thing worked with the wheel! I couldn't believe it, I think he was pretty suprised as well.
Anyways, just thought I'd post a followup in case anyone else has this problem.
allison.