I'm sorry you're going through this...it's very stressful, and doesn't make for very safe driving....
Harry was like this when he was a pup, but it seemed to calm down once he hit 2 years old - I think with him it was also over-excitement, knowing he was going to his 'nana' or somewhere else nice....he just couldn't control himself.
However, your Littlie is 13 years old - so what else can you try?
I wonder if you've tried one of those 'calming' diffusers? I never did, but have heard good things about them. Also, others swear by Thundershirts - again, I've never tried one, but I believe there's a complete money-back guarantee if it doesn't work.
Harry goes in a crate in the back of my car, and HE seems to have got better once I secured him more inside. He has his harness on in there, with a seat belt adaptor clipped to it and plugged in, then the whole 'human' seat belt around his crate so it can't slide around.
I really, really wish you luck and hope you find a solution - I know what a nightmare it can be.....
Sally + Harry x