I know I'm not supposed to care what she thinks, but I'm worried if she see me without my wedding ring she will thing I've already thrown in the towel.
I wouldnt wear it or remove it to get or not get a reaction out of her. There is no way to know how she will react, so there's no reason to try to base your actions off of her.
I would recommend you consider why you are wearing it and decide whether it is a practice you want to continue for yourself.