Your W does not want to be friends with you, in fact she seems devoted to being as miserable, angry and mean to you as she possibly can. She pushes your buttons at every opportunity and revels in it when you respond in kind. So quit responding in kind! Be as businesslike, detached and unemotional with her as you can. I think it will be much better for your emotional well-being in the long run!
I can vouch for this. There's nothing like the satisfaction of not rising to the bait or stooping to their level. Listen to AS.