Well, so... she's not being traumatized by the car ride. Here are some suggestions.
You have a crate. Put it in the way back of your car (I think you have an SUV? Can't remember.) Put the dog in the crate. Then...
1. Crank up the radio, 8 track tape deck
CD, MP3, whatever and attend to that and stop worrying about the dog.
2. Ear buds and books on tape on your kindle. That's my personal favorite.
You can always buy a pick-up. Crate her in the back and drive however you like.
Really. The dog is fine. Don't stop the car. Don't pay attention to her. Sounds like a field bred lab who knows there are no birds to retrieve as long as she's in the car and she wants you to get to where you're going because... who knows? Something fun might happen.
Doesn't sound like she's cringing around the car before the ride or afterwards. No excessive salivation or puking in the car. No wetting herself. She gets in the car without resistance. She hops out of the car looking for the next fun thing... Relax! She's just excited.
There are ways to MAKE a dog lay down and be quiet. I think she's a little old to start on that. Really, it's probably a lot better to work on you.
Have you ever had kids? Sheesh, I'd take a whiny panting dog over... "MOM... She's looking at me!" "He touched me first!" "Did NOT!" "Did, too." "Move over." "You're on MY side. YOU move over". "MOM
!!!!"