Ovidiu,
This is not an uncommon problem, especially when the pup’s initial exposure to cars is negative. I have also worked with dogs, however, who did not like cars even though everything was done “right” from the start. Zvonimir gave some good advice. I’ll add a few other things that have helped with dogs I have worked with.
1) Like Zvonimir said, start giving the pup his meals in the parked car. To start, it might help to have both doors open (have the pup on leash or some other way to ensure he is safe if he happens to hop out!). This helps relieve the pup of being “trapped.” When he is eagerly hopping into the car for his meal, you can start having one door closed. When he is comfortable with this, close both doors. Then you can start feeding him while the car is running, but not moving. Then just drive around the block and come home. Take your time with each step, and if possible, avoid having to actually take the pup somewhere during this period. You are starting to recondition him to the car, so it will take time.
2) You said you have a hammock. I have found that the older hammocks can be a problem for some dogs. They are more of a “U” shape, and tend to roll the dog around. Some dogs are very uncomfortable with this unsteady surface. Some of the newer hammocks are designed to lay flat on the seat with “anchors” that tuck between the seat and the seat back to secure it firmly on that side. There is less rolling of the dog, helping the dog feel more secure.
3) Just like humans, some dogs are more prone to car sickness than others. This can make any trip in the car miserable, no matter what you do. Signs are typically anxiety, drooling, and possibly vomiting. If you can find ginger snap cookies with real ginger in them (many commercial varieties don’t actually contain ginger!), you might try giving one to the pup. You can also use either benadryl or dramamine for dogs, but be sure to check with your vet for the right dosage. Don’t feed your dog right before taking him for a ride if he is prone to car sickness.
4) Once you do start going for short drives with him, always go someplace REALLY fun for him! Take him out, play with him, let him sniff and explore someplace new. You want him to learn that car ride = fun time coming.
He may never learn to love car rides like some dogs, but he should at least learn to tolerate them. If you do all the above and he is still very stressed by the car, you might need to talk to a veterinary behaviorist about using anti-anxiety medications for a while as you continue to work on counter-conditioning him. Good luck!