Time for my Kevin Shasteen impression.
Terry, your theory is sound. What occurs at the point of contact is called an 'instantaneos center of zero velocity'. Basically the rest of the tire is basically pivoting around the I.C. at any given time. (of course, the I.C. is constantly moving as the tire rotates as well)
Now the velocity of the center of the tire is for our discussion, the same as the velocity of the vehicle, in this case 200mph.
w=v/r : rotational velocity=linear velocity/radius. w is constant everywhere on the non-accelerating wheel, while v is different depending on how far from the I.C. the point in question is.
Just for $#!+$ and giggles, if we assume a 25" tall tire, the tire sees a rotational velocity of 290 rad/s. (forgive me for not showing my work) Or 46 rev/s. Thats a cool 2760rpm.
Back to Einstein. The stationary observer will see you and your car moving at 200mph. They will see the top of the wheel (directly across from the I.C.) travelling at 400mph. You (in the car) will see the top of the wheel moving at 200mph, and the stationary observer moving at 200mph.
As far as centripital acceleration goes, its dependant on the distance from the center of rotation. This is because its not instantaneous, but sustained. (remember the last example is only for in INSTANTANEOUS center, and that center has a new position around the circumference of the tire for every instant) In this case, you must consider that the wheel is rotating around its center. The wheel will grow uniformly in all directions, even at the bottom. (granted the weight of the car will slightly affect the shape and growth)
Hope that helps visualize. I do highly recommend the book Johnc mentioned. I don't know what he means about it being boring though! (engineers are funny that way)