Just remove the seat cushion (takes one minute), rinse the soap out of it, and let it dry in the sun for a day or two. A long time ago my cat peed on the back seat of a previous car of mine, so I removed it specifically to soak it in enzymatic cleaner. After thorough rinsing, I let it sit in the sun for a couple of days. It was good as new.
You can remove the door card and do the same, or just leave it on. It will dry on its own. It's not like the seat cushion in that it hasn't really absorbed a significant amount of water.