X2. Talk to the manager of the car wash.
Car washes are incredibly variable in how they deal with this. Some take a "use it at your own risk approach," others will cover damage caused by their equipment. It varies a lot.
I guess you could call the manager but I see 99% of the time it would be a fruitless attempt.
Chalk it up as a lose, go down to the junkyard and get another miror and if need be use the manual service carwash until it pays the difference. To bad the mirrors didn't fold back. Many theses day do and its always a good thing to have in a car.
Only outcome I see coming out of a call is either #1 we are not at fault, or #2 how do I know it wasn't broken before you used the car wash.
If my a miracle chance they do replace it I would use only that carwash.
It's odd that a car wash would do such damage without an underlying defect (eg rusty screws, etc), but IME, it's three screws and a gasket or two. Not much to it. Removing interior trim prone to cracking or getting dirty. And, of course, getting paint matched is a trick and expense, depending upon paint color.
The few I`ve replaced were just held on by a few nuts on the inside of the car behind a plastic cover that hid the bolts on the mirror . I bought the replacement mirror on ebay around $35 . On my Altima I had to get a can of matching paint made from a Car paint store. The other 2 times they were a gloss black and came that way from the seller.
i managed to get a screw to hold mine on,there is really nothing to screw onto but it worked, still holding over 1 year now
mirrors on ebay are cheap but you have to take the door panel off to install them
Looks a lot like the one for my wife's Windstar. The replacement came with the black plastic sail piece that fit to the window frame. I popped off a trim piece on the inside, undid three nuts and disconnected an electrical connector. Assembly was the reverse, very easy.