Have you assigned the in-game GTA controls to the same keyboard keys assigned in xpadder?
For example:
In xpadder assign the left trigger to the down arrow key, then in GTA go to your keyboard config and assign the 'reverse car' key to the down arrow. Then when you hit the left trigger the car should reverse. Right?
The interface on xpadder will tell you if it detects the triggers, so if you have a defective or sticky trigger then you'll notice on xpadder that the trigger indicator will not light up (as it does when you press other joypad buttons).