In desensitizing her to the car, you want to start with short periods of time.
Car sick puppy
has a post in there with a link to an article about it.
I have a carsick dog (adult - has some brain issues for real) and I have had him in the car with me, just sitting, while I was on the phone and he started the lip licking and drooling after we had been in there a while. So we went over his time, without Cerenia on board. I believe the link in that link will detail it.
If you are going to the vet, and know when your appointment is, you can adjust her eating/poop schedule accordingly. ETA - however, nervous poop is always seemingly available, in some kind of colon pocket so there is nothing you can really do about that other than to start reducing the anxiety as much as possible. Cerenia has been THE thing that works for my dog (pills) like I said in the posts linked, but not sure how old a dog needs to be.