For some reason, Toni's ma wants him to enter a race against Dan Sucho, a good man in her eyes.
You will be racing Sucho in his Thunder-Rodd and two others in Stallions, a Leone Sentinel is enough to win. At the start, everyone vies for 1st place but once you're there concentrate on the next move. After beating him, he'll drive off and you need to chase him down. Bash his car until he exits, then you can just run him down.
You can now do car races. There's one activated in Trenton outside Don Kiddick's Sausage Factory. Also, the Thunder-Rodd will spawn outside the Old School Hall, Chinatown after this mission.