I don't think you're nuts. My little one did fantastic on car trips when she was 2 1/2. Just plan on stopping often, and try to find hotels along the way with a playground so she can stretch her little legs. We brought her favorite toy, a soccer ball, along for rest stops to take in a good 10 minutes in each of their little grassy areas. We also brought a portable DVD player for an occasional movie and some of her music for the trip, DH wanted to beat his head into the wall after sooo many hours of the Wiggles, but hey, she was content. Also, I opted to diaper change in the backseat in the parking lot rather than inside the rest areas themselves.
I do, for the record, think my parents were crazy when they packed me (3) and my sister (10 months) into our un-airconditioned car (a pinto) and drove us from Cincinnati to Siesta Key Florida. Something they will never, ever forget.