> We go to the beach every day for her exercise
> I am sure I have done something wrong
Hi Sally, no you haven't but your regular routine has allowed her to learn exactly what happens next, and she is simply getting over stimulated by excitement.
If she we mine I'd be inclined to stop the beach walks for a while. I'd walk her from home, no car journeys for a week at least. After that I'd probably do another week walking from home, but I'd add a short car journey after each walk - just round the block. Then perhaps a short car trip every 2 days to a different walking destination each time. Depending how she reacted I'd either go back a step or two or move forward slowly.
I'd also look to amend my cues - such as picking up car keys, putting on a coat, putting on walking boots, collecting the towel etc. All of these are things that tell her it's about to happen.
I think the training term for what I'm describing is desensitisation (?). You do need to break her habit, it's both dangerous and annoying for you but to her it's self fulfilling. I believe a car crate is a safe idea and keeping it covered may help. Good luck