Can she see out of the car when she is in your lap? If not, maybe a carrier or crate on the floor of the passenger seat would work. It could be the visual stimulation upsetting her, and she could still see you from there if you think that helps her stay calm. It is very unsafe to drive with a dog on your lap, but I wouldn't want her to be sick either! Many puppies outgrow carsickness. I had a foster that got carsick every time we were in the car for more than a few minutes, but she outgrew it.
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First time Chihuahua owner with many years of dog experience!