Maybe I'm too old or my family was weird. We called it "le carwash" with a beautifully French "carouache" pronunciation. But yeah, "lave-auto" sounds more familiar.

Honestly, If anyone asked me "T'as fait quoi?" I'd blurt out "J'ai amené ma voiture chez le lavage". Background: I stopped speaking french when I was ten and my family isn't native, but it feels more conversational than "station de lavage".