Hello, my name is***** and I have over 20 years of experience as a veterinarian. I'm sorry to hear about your pup's motion sickness.
Dogs are prone to car sickness as their sense of balance is much better than ours and as such they are easily affected by the motion of cars or boats. Some dogs do outgrow it, but if she is 2 years of age she likely isn't one of those.
Even though she doesn't seem anxious now we don't want her to associate the car with negative things so try to keep trips short and as positive as possible. Some dogs get stressed if the only places they go are negative, such as a veterinary clinic. By making the destination enjoyable she may feel less stressed/excited, so less likely to move around. Dogs that lay quietly are less likely to get sick.
You can give Gravol also known as Dramamine (dimenhydranate) for carsickness. The dose is 4mg to 8mg per pound of body weight. Give it an hour two before travel. It will last about 8 hours. Side effects are mild sleepiness and dry mouth. I see this is something that you are already doing. I would continue to do so to try to lessen the chances of her associating the car with nausea and developing anxiety.
Or you can try Benadryl (diphenhydramine) at 1mg per pound of body weight orally. Side effects are sedation and dry mouth as well. It should be given an hour or two before travel
I do recommend that she not eat for 8 hours before travel if the car-ride will be long. Ice cubes can help to quell nausea too and keep her hydrated.
I also recommend keeping a window cracked as fresh air seems to help too.
Some dogs do better if they cannot see out of the car, the moving landscape seems to make them dizzier and thus more nauseous. Try and get her to lay down in the car.
If this doesn't work discuss a medication called Cerenia (maropitant) with your veterinarian. It works very well and lasts at least 8 to 12 hours.
If you believe any of this is all anxiety related, although it doesn't seem likely with her, you can try products such DAP (dog appeasing pheromone) which is a synthetic version of a calming pheromone nursing bitches produce. It comes in a spray as well as impregnated collars. Another option is a calming homeopathic remedy called Bach's Rescue Remedy. It can be used along with DAP. See this link for further information: http://www.bachflower.com/Pets.htm
If she is young, less than two then she may indeed outgrow this, so continue to keep things positive and see what happens.
Please let me know if you have any further questions.