Option 2 is very very inefficient compared to option 1. You would effectively have to do it on the cpu since you can't really return vertex data from the shader (and it would likely be in a different space if you could).

Define your wheel so that it's axis is at 0, 0 (i.e. top might be at (0, 1), right (0, 1), bottom (0, -1) and left (-1, 0). Now you rotate it using whatever method you choose (a single axis rotation is quite simple). Then you translate it to it's actual position. A rotate->translate matrix is quite neat to do when you are dealing with 2D, you could make it in one go rather than making 2 separate matrices and multiplying them. All you'd need to store is position and angle and build it from there each time one of the values changes (but no more than once per frame)

It's important you define your vertices like that and rotate first BEFORE translating as otherwise you will be rotating about the wrong point.

A matrix to do that would look like this:

cos(A)   -Sin(A)  x
sin(A)   cos(A)   y
0        0        1

Pad it out with extra zeros and a 1 (for the bottom right element) if you need a 4x4.

Depending on how you want your circle to look you can probably use the same shader for both parts (especially if it's just made of lines). As for using your points later, you wouldn't really be moving them, you'd be keeping track of just the position and angle which is then used to move the original vertices to their current position each time.