If I understand you right, you wanna have a route from Google Directions, which should match your determined route.
Well, it could be hard to manage that because Directions is designed to find the shortest path between two points. One way is to use the option of waypoints, to limit the suggestions of the API. Simple said, don't use just a origin and a destination. Use as much waypoints as you have to between the origin and the destination to get the nearest route possible.
Getting the exact route as you think of it is just big luck.