Hi there and welcome. Take your girl with you in the car on short trips as often as possible so that she doesn't build up an association of going places that might make her anxious (like the vet). Drive somewhere, get out to take a short walk and then get back in and go home. Build up the time and distance as she starts to relax with the shorter trips. If you expect to make that longer trip frequently, you may want to invest in a hammock for the back seat of the car. It will protect the car seats from damage from nails, accidents of various types and dirt. The further back in the car the dog is, the bouncier it is, so put her in back seat if you can. I would use a harness to restrain her, so she can't climb into front seat or attempt escape. All this assumes you aren't crating her in car, of course.
Lily AKC: CGC CD HIT CDX RN RA RE RAE RAE2 RAE3 NAJ NA; APDT: RL-1; CPE: CL1-R, CL1-H, CL1-F, CL1-S, CL1
Peeves AKC: CGC BN RN