This is almost exactly what happened with one of my cats about 3 weeks ago.

Basically I put a cat bed in a place I had never put it before and for some reason one of our cats, PC, thought it was a new type of litterbox. He started to pee in it, but fortunately I saw him and stopped him just in time. I took the cat bed away and moved it to a more "normal" spot and all was fine.
There hasn't been a problem since.

PC is completely litter box trained and has never shown any problems before and has not had any problems since. The new location of the cat bed just seemed to have confused him a bit. It sounds like the fabric covering your car seat is very similar to the fabric on the cat bed - there must be something about it that attracts them in a certain way.

Donna