Some of that is easy to do - the wheel tracks don't ever define the outer envelope, for example, so those can be excluded from the alpha shape. But even using only the outer points on the vehicle body, you still have to find a way to pick the inside ones and remove them to be left with just the outermost boundary.
Consider a tractor / trailer combination with four points on each body. That's eight outer tracks (four on each side) which will defined the total envelope. As the tractor / trailer turn and move, each of those tracks will inevitably be the outermost track and define the limit of the envelope.
The issue I can't get past is that an alpha shape will leave me with the same problem I begin with - determining which points are outermost so I can have just a boundary, even if it does create a nice mesh. Solving that would require the same approach I would use if I never used alpha shapes to begin with...
That said, if there's some other way to hide the mesh interior (or generate a poly line that represents it's boundary) using the alpha shape library, I'm all for it.
In the end, it's really only an aesthetic issue - I don't want to see a triangulated mesh for the swept path boundary. I might even consider using the boundary vertices as points for a spline to provide smoother edges, but that's another matter entirely.