Sometimes engine shuts off when change gear from reverse to drive

I have the SE model. The car was well maintained and is running well, except the following problem for which I have payed a lot of money and the problem still exist:
Sometimes, when going from parking to reverse, to drive the engine shuts off.
Here are the sequences of events:
- The car is parked with engine off.
- Depress the brake and Start the engine.
- Change the gear from Parking to Reverse.
- Release the brake.
- The car is moving back in reverse.
- Apply the brake.
- Change gear from reverse to drive.
- Release the brake.
- The car does not move forward and the engine shuts off.
- To restart the engine I have to push hard the acceleration to increase
the rpm over 4000.
- The car restarts and a big smell of gasoline is inside the car.
- If I do not accelerate hard when I turn on the key, the engine not will
not restart.
Once the engine will start all is okay for an undetermined period of
time.

The problem is that when changing gear from reverse to drive the engine shuts off. There are no on board malfunction lights on.