I have the answer to your problems
Go to your supermarket.
Go to the bug spray aisle.
Check the lids on the bug spray.
There is a brand of bug spray that comes with an "extension nozzle" (like WD40)
You extend the nozzle, and spray it into the areas where regular surface spray cant reach.
Inside vents, in behind external mirrors etc (mirrors are where i used to have a spider problem)
Washing the car won't get rid of spiders.
They mostly only come out at night, and seeing as most people wash their cars during the day, the spiders are safely tucked away in bed where you can't get to them.
Spray everywhere you see webs.
If possible, leave the webs on the car, and spray the webs.
The spiders will crawl through the spray, and die.