I always kept my ring on. H took his off sometimes and put it on at other times: I think it depended on his mood. I tried not to look, to check, to let it affect me but it was hard. I doubt, in our case, my wearing my ring or not would have made any difference to how he felt or acted, but I'd decided I wanted to act as if I was married in terms of my relationships and boundaries with other men so long as I was legally married, and my ring reminded me of that. It mattered to me. I think you should go with your own values in this area.
Also - a question. When she asks 'when are you going to let me go?' what is it you thinks she means? Does she want you to arrange a divorce for her and take care of all the financial stuff? In which case, I would let her handle all that herself given she wants it, but don't do anything to sabotage her or stand in her way. If she means 'give me space' or 'stop acting like we're a couple' then I think you have to respect that, 100%, from today.