Toni grabs a four-door vehicle and drives to the petrol station in Harwood. After entering the petrol station, the Leone Family gang members get in the car and Toni drives to the Pay 'n' Spray in Red Light District and loses the police. Toni then drives to Vincenzo's warehouse in Atlantic Quays to complete the mission.
Any vehicle brought to Vincenzo's place will disappear after the cutscene. In order to continue the mission, a four-door vehicle must be obtained. There is usually a black Kuruma parked right next to Vincenzo's building. A "Leone" health bar appears after the cutscene and begins to deplete, so the player needs to obtain a suitable vehicle as quickly as possible.
The most likely cause of mission failure is driving over a spike belt, which renders vehicles virtually uncontrollable. (This also applies to the Hot Wheels mission that follows.)
The mission will not fail if any Leone members get yanked out of the car - just head to the Pay 'n Spray to lose the heat then come back and pick him up later. The wanted level won't come back.