Well, I assume that completion of the objective is triggering a trigger already. You just need to unlock the vehicle at the same time:
Vehicle to unlock should be named
myVehicle and have init of "this lock true".
Trigger type and Condition: Whatever is appropriate for your objective.
On Act: "1" objStatus "DONE"; myVehicle lock false
Since mission-placed triggers are global, this will work fine in MP too. You may find the
Triggers chapter of our editing tutorial useful.