Dog
I probably should have been a bit more detailed in my post. "Dog" is not a mispronunciation, or a regionalism. It's the actual name of a piece of equipment. Once upon a time, wheels were tied into position, Shortly thereafter, however, ship's wheels have had a hinged catch that fits into a ratchet to hold the wheel in place.
This hinged catch is actually called a "Dog." This is its actual name.
Ship's wheels are turned only when the pilot needs to change course, or needs to maneuver around something. Contrary to what you see in some movies, there is no need for a pilot to stand there and maintain a course. You turn to the heading you want, and you then engage the dog into the ratchet.
So "dogging the wheel" is a proper term. It means turning the wheel to a certain heading, and then engaging the dog to keep it there.
I don't believe turning a car wheel by hand would qualify as "dogging the wheel," and it would throw me a little to read it, but I suppose it would ultimately be the writer's decision.