Dog panics in car

Try getting her used to the car get her comfortable outside of it. Treat when she not panicked. Begin beside the vehicle. If she is ok there, put her in the car with door open, her leashed, treat until she is comfortable and doesn't feel trapped. When she is ok with that, start the car, treat, take as much time as she needs. Then short rides, even if you just pull out of the drive and back in. Make the reward being in the car, or at it.
I spend alot of time at training g, so the pups or dogs that don't lime to crate or ride get used to it fast.

Even better, clicker train her so you reward at any motion towards the car. Then near the car. Then entering the car. That way, instead of you putting her in the car, she get to control the approach. It would probably work the fastest.

I would also have "car parties" inside of a turned off car and not start driving at all until she will eat a meal in the car. If she won't eat her dog food in the car, she is still worried. I wouldn't turn the thing on until she is past that.

Is she afraid of getting in the car or do you just put her in and her reaction begins when? When the car starts? When it starts moving?

Start with making getting into the car a fun game. Use treats, toys, and an exited tone. Leave the back doors wide open and climb through with her. Once she's comfortable in and around the car, move on to doing the same stuff with the car started. Only when those stages are complete should you take her anywhere. When you do take her somewhere, keep the distance short at first and always make the destination a fun place until she looks forward to car rides.
My beagle used to be terribly car sick when he was a pup, but with time and patience even he will happily hop in the car.

My Zoey still does this on very long rides....sometimes she even pukes. One thing that has helped is very short, frequent rides with something good at the end....for us, if weathers good I take her with me to get kids from school....short ride, and she gets a gaggle of teens loving on her once we are there.