Don't put the dog on your lap, it's not very safe.
Sure she will stop crying, so did my cavaliers when they got what they wanted and
both ended up on my lap (even better if the window was open a bit for them), but it is not the safest choice and you should avoid it, especially in the front seat. Sitting on laps in the back is bad enough, but the front is so much worse, I always got angry when me family let the dogs sit on laps in the front passanger seat. You can just imagine them flying out the front windscreen if there was a sudden stop.
You could try harnessing the dog and seatbelting it in so it can't move much. Being harnessed helped with my cavaliers (although they would still whine, it wasn't as loud or intense), it meant they could not ask for attention or to sit on laps or move around the back seat.
That's why I think it's an attention thing, because they didn't cry when there was no other passangers when in the back
or front (no one to give attention) and cried less when harnessed in (couldn't walk over to the passanger and ask for attention).
It's easy to see how the dog could learn this behaviour too - when the dog is young and getting used to the car it cries once so gets a pat or cuddle (or even a "shhhh") to "reassure" it. So the dog learns that crying etc, earns attention in the car. I'm pretty sure that's how my cavaliers learn't that behaviour (and they would already be excited about being in the car which made it all so much worse).
I would be careful about "distracting" the dog in the car by giving it treats, doing tricks etc, it could just increase the excitement assossiated with the car and mean that the dog is being reinforced by giving it attention in the car (if that is in fact what the dog is after). Then on longer trips you would be having to entertain the dog the entire trip
With Holly, we harnessed her in right from the start and never gave her attention in the car (we're lucky she didn't learn the whining from Paris). But I don't think Holly would have had a problem anyway because she seems to hate being in the car (pulls away from it when it's time to get in) so she falls asleep as soon as the car starts (I guess that's her coping mechanism). I have wondered if the car makes her feel a bit sick, but she seems fine when she gets out and she just sleeps (even in the front seat) so there isn't much I can do about it.
I hope this helps
