Carrying your dog in your lap is very dangerous. If you're in an accident, the force of the air bag can kill your dog. And if that doesn't, getting ejected can too. It's best to always keep your dog buckled up in the car.
If seeing out the window helps your puppy's car sickness, look for a dog booster seat for the car. It is a little seat that keeps them secure in the car but high enough up that even small dogs can see out. Just google "dog booster seat" and you'll see pictures of them.
For the car sickness, how soon are you going in the car after feeding? If there's a small gap between feeding time and car rides, try feeding 3-4 hours before you go in the car. That will help too.
Hope that helps.