I think to remove the faucet you will need to access the back side of it. Some RV manufacturers provide a means of access, and some don't. Look for a panel on the other side of the wall behind the faucet. If there is none, you may need to cut a hole and install a panel afterward. Access panels in various sizes are available at home improvement stores, or you can try to make your own if you are handy.
Some RV manufacturers provide access with a water-proof marine screw-in deck plate right through the shower wall below the faucet. Another option would be to cut a hole below the faucet and install one of those if there is no other access.