Just last night I took my truck through its first automated car wash. I thought of exactly what happened to you as I entered since there is a super long, fat, round guide bar on each side the entire length as you drive through. I forgot to push in my trailer side mirrors (my 08 didn't have them so it didn't even cross my mind until the washing unit came towards me. I rolled down the window with soap flying in and got one in but the other bashed forward from the machine. ARGH! I wanted to get out during the wash to see what happened! So, I know how you feel. I was then drying the truck and thought the 'chrome' rims seemed plastic. Oddly enough, while searching for parts for it on Ebay, I did come across a listing for 'chrome' wheel coverings for the 2011. I thought at the time, "Wow, what a cheap way to make non chrome wheels look chrome." I then wondered how they would stay on. So, maybe that is the 'chrome cap' our rims have? They call them skins. Is this what we have?
Here is the link. If the link doesn't work search under 2011 Ram Wheel Skins.