Vincent's actions somehow serve the Grand Plan.
The Director could have overwritten him when his wife took a picture of him, but instead chose to (with uncharacteristic wastefulness) kill his wife in a way that seems almost calculated to make him want revenge. It also allowed information of the Traveler conspiracy to spread in the second season finale, which several characters noted it could easily have prevented. The simplest explanation is that the Director is playing some sort of Batman Gambit, and that everything Vincent does to fight it is somehow going to end up instrumental to its success.- Further fueling this theory is that the Director overwrote the partner INSTEAD of Vincent when he clearly had a lock on him, and sent yet another message through his son instead of overwriting Vincent. Finally, the Director did not overwrite the Vincent body until AFTER Vincent had already transferred his consciousness into the Doctor. The Director could have easily prevented the transfer by overwriting the crazy Traveler in the schizophrenic body when he was inside the Traveler hideout - who was going around announcing he was from the future and drawing pictures of it, and who also happened to be the ONLY one with the knowledge to help Vincent. The Director clearly has some kind of plan for Vincent that doesn't involve just killing him. Even the message that he sent Vincent is suspect 'Traveler 001 you are off mission', is not exactly a big threat.
- At the beginning of 2.12 when he watches home movies, Vincent is clearly shown in one of them.
- Considering Vincent's later actions in the series and where they end up, with MacLaren declaring the Traveler program a failure and the Director concurring, it is possible that the Director was trying to ascertain if Vincent himself was a root cause of several serious problems that could have been avoided by cutting him out of the equation completely. He's doing this the same way he came up with many of their solutions: by letting things play out before moving on to the revisions.
Vincent would have originally killed both his wife and business partner in a rage had they not been taken over by the Director.
The Director is shown to be pretty consistent about not killing those who were not already scheduled to die, even in situations where it would be obviously beneficial. It's unlikely that the Director would choose to kill two innocent people who would otherwise have survived while leaving Vincent alive for no reason. However, Vincent was shown to be getting increasingly freaked out at both his wife and business partner in the moments before they're taken over. It would make perfect sense for the Director to choose to take over two people who were about to be murdered in order to send a message while leaving Vincent alive, since Vincent wasn't destined to die at that point. The Director is also shown to have built-in limits on when it can execute Travelers by overwriting them even when they've gone off mission, and Vincent may well have not yet met the criteria for an execution instead of a message.