I presented the problem to my father, a landing gear specialist for the F-15 among other Boeing military jets.

He affirmed my notion that the rear axle is along the line of the turning circle radius.

The front axle would also be in line, and the angle between the 2 axles implies a point of intersection, which is the center of the turning circle.

Furthermore, no matter how many axles there are, they should all be aligned on the same point at any given time.
(accepting that when you are not turning, they are aligned at a point "infinity" away, and it's equally infinitely away to the left as to the right.)

Modern cars have 2 front axles and 1 rear axle (geometrically- not in terms of parts).
The steering that accommodates this must turn the front wheels at slightly different angles to prevent slipping, which is noisy and embarrassing in the best cases.
If you are on a slippery surface and your wheels are not properly aligned, then the vehicle will alternate between the available turning circles in a chaotic pattern.