You can try to check the Directions API if it can do the things that you want to achieve. If the Distance Matrix API is a service that provides travel distance and time for a matrix of origins and destinations, the Directions API is a service that calculates directions between locations. But it also contains information like travel distance and duration.
Here is a sample request using Directions API:
https://maps.googleapis.com/maps/api/directions/json?origin=Dodger%20Stadium,%201000%20Vin%20Scully%20Ave,%20Los%20Angeles,%20CA%2090012,%20United%20States&destination=STAPLES%20Center,%201111%20South%20Figueroa%20Street,%20Los%20Angeles,%20CA%2090015,%20United%20States&key=YOUR_API_KEY
Just take a look at the legs and steps part. These two is a part of waypoints that can give you a small detail about the directions.
legs[]
contains an array which contains information about a leg of the route, between two locations within the given route. A separate leg will be present for each waypoint or destination specified. (A route with no waypoints will contain exactly one leg within the legs array.) Each leg consists of a series of steps.
Each element in the legs array specifies a single leg of the journey from the origin to the destination in the calculated route. For routes that contain no waypoints, the route will consist of a single "leg," but for routes that define one or more waypoints, the route will consist of one or more legs, corresponding to the specific legs of the journey.
steps[]
contains an array of steps denoting information about each separate step of the leg of the journey.
Each element in the steps array defines a single step of the calculated directions. A step is the most atomic unit of a direction's route, containing a single step describing a specific, single instruction on the journey. E.g. "Turn left at W. 4th St." The step not only describes the instruction but also contains distance and duration information relating to how this step relates to the following step. For example, a step denoted as "Merge onto I-80 West" may contain a duration of "37 miles" and "40 minutes," indicating that the next step is 37 miles/40 minutes from this step.
Just read the documentation about Directions API to know more about it and the things that you can do for this API. I hope I give you a small idea about this. Goodluck :)