HI,
Yes, most dogs do get sick the first two times they get in a car. Mine did at first. But the more you take them out this should stop. I make an effort to take my yorkie on a ride at least once a week. And he loves the window slightly cracked. He seems to love the wind in his face.
The vet told me to give them a half of Childrens Benadryl to calm him. But i never did this. I just him used to the car by taking him out quite a bit.