I like the idea of asking her for you two to sell it and split the proceeds. If she is a classy woman, she will say, "No, you sell it and keep the proceeds" particularly if she was the one who initiated the divorce. Yes, legally, she is not required to give it back to you, but a good person would give the ring back (unless you cheated on her and that was why you two divorced).
Anyway, I would approach her nicely because you will get a more positive response from her by being nice than by demanding her to split the proceeds.
Let us know what happens. Her true character will come out in a situation like this.
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