Don't drive away until she is laying down. Tell her to lay down and stay, then start driving. If she gets up, stop the car. Wait a few minutes, tell her to lay down and stay again and then start driving. Rinse, repeat. She thinks you cannot stop her when you are driving, so you need to change her mind by stopping and reestablishing control (having her lay down and be calm).
You kind of want her to have the idea that laying down makes the car go, and standing up makes it stop. Don't worry about her having to lie down the whole time. My Sam does. Unless you are driving for hours, it is not too much to expect her to lie still.
Definitely perfect this in a parking lot near your house before taking it on the road.
Also, how is her attitude toward the car in general? Does she charge up to the car and leap in? Do you make it sound exciting to her? If so, she could be having more built-up excitement than she knows what to do with. She should be calm before she even gets in. Put on her leash and walk her calmly to the car-dont tell her where you are going, or ask her to go for a ride. Have her stay before getting in or out until you invite her in or out. Get some treats, stand outside her door and ask her to obey sit, down, shake, whatever she knows that is easy for her to do in the car. Practice to help establish that the car is a place to be calm and obedient. If she heels, have her heel right up to the door of the car before getting in.
Dog trainer Patricia McConell used a similar method to keep her BC from barking on the way to sheepherding. She actually got out of her car and read a magazine til he stopped barking.
She said it took forever the first time, but eventually they could drive to the sheep bark-free.
Good luck!
Marie