when you get in the car with him, dont be hesitant and expect the worst, him barking and biting. if you remane calm and assertive and ignore him when hes in the car and dont give into him when he plays up.

if you let him out of the car when he is barking and biting then he will think it is ok to do it everytime and you will let him out. you should only let him out of the car when his brain is calm, not barking and not biting.
you will know when his brain is calm, because he will look a little dosile and may start to shut his eyes!

is your pup potty trained on paper?
if he is then i have a suggestion, put a few sheets of newspaper on the floor of the car. this works with most pups and dogs, because they know the sound of the paper, know the smell of the ink and it acts like a soothing agent.