Burn the car. It is the only way to ensure it is dead and no little baby spiders with giant genes are breeding in your air vents.
Seriously though, you did well to not cause a wreck.
I totally understand your panic. The surprise is unpleasant. I was on the loo last year and heard the extractor fan above my head stutter. I looked up thinking there was a short I would have to see about fixing but then I saw this big spindly, hairy leg poke out of the extractor fan. I was so confused...then it turned into a scene out of a horror film. This massive spider crawled out of the fan!😨
A spider, so big, it caused the fan to stop.
It dropped down from the fan and landed on the floor between my legs.
Well, I lept up and staggered out of that bathroom mid job. Knickers and jeans around my ankles and shouting blue murder. My other half came running and when she saw the beast she closed the bathroom door in a hurry and helped me get myself to rights. I was honestly afraid it was big enough to open the dopr itself.
After a good laugh at the predicament I went back in there with a broom and murder on my mind. Spider Rex died a most brutal death.
I then went into the attic and sprayed the place down with spider repellant, lemon spray and vinegar. Then I set up numerous sticky insect traps, unscrewed the extractor fan and doused its innards with lemon juice.
The bathroom smells great and is still spider free.
I recommend dousing your car with citrus essential oils, insect repellent and some lemon juice in the vents....either that or burn it to the ground.