Starting after Contract 01, you'll have some free time before driving off to your next assignment. This and three other trophies can be obtained during this time:
Your mother may be in random locations throughout the story. She might be sitting on the couch watching television, in the kitchen cooking, outside grilling or watering the plants, or elsewhere in the map; she will always be able to be talked to, much like interacting with the television or radio, so if you have done everything but that, check the surroundings for her pink blouse or gray hair.
Do note that there is a point in the game where you will be unable to do this without restarting on an earlier contract. If you don't get this through normal progression, simply choose Contract 01 again and go back through it all.