Gentlemen, let us discuss and orchestrate a tactful and dignified way to ask for the ring back. Despite what you have been told (probably by her and her shrew friends), in some situations, you are actually entitled to get the ring back.
Here's the situation... she wants to keep engagement ring for some reason that has nothing to do with anything legitimate like:
1. she was truly screwed-over by you
2. actual prescribed etiquette dictates that she gets to keep it
3. she really needs the money from the sale of said ring, and you're a generous guy who at one point loved her enough to marry her so you're going to let her sell it and keep the money
I think it's perfectly reasonable to get the ring back provided no deal was sealed, there was no marriage and you didn't do anything unforgivably heinous to her.
To the victor go the spoils, right? There's no victor here. There are two people who feel like they've been defeated. Period. So why on Earth would someone want to keep the spoils of such a sad war? WHY?!
I have meditated on this at length and have pretended in my mind that I am some loon that wants to keep the engagement ring from a marriage to a kind and decent man that never happened. After much thought, I determined that there are only a few demented reasons I would want to keep the ring even if everyone (except the shrews) is telling me to give it back. Even my therapist is telling me to fork it over, in the interest of "closure."
The twisted reasons for keeping the ring are generally one of the following:
1. I still love My Ex-Fiance, but I realized eventually he would figure out who I really am because he is smart and can't live in the dark forever. Plus I know he's too good for my disingenuous black heart. Keeping this ring will help me to feel better. Not sure how exactly, but I am okay with deluding myself into thinking that it will.
2. I'm shallow! I like shiny things and I want lotsa diamonds! I can take the stones and make a pretty necklace! Maybe I could have it sized and wear it on my right hand! Right hand rings are hot now! And I'm too daft to realize that an engagement ring on the right hand and nothing on the left makes it look like this: I am wearing my engagement ring on my right hand because I am greedy and I still love my ex-fiance and I kept it and I am too cheap and still too in love with my ex-fiance to have it reset.
3. I'm a vengeful, vindictive, resentful main dish of neuroses with a side order of immaturity and insecurity.
4. I still love My Ex-Fiance.
Hmmmm. Okay.
So guys, taking into account what you're dealing with here, I think a humble and gentle yet direct approach is best, like so:
"Ex-Fiancee, I think it's time for you to send me the (use "THE" and not "MY" or "YOUR") engagement ring back. It's of no use to you any more and frankly, I could use the money for the house." (insert: car, travel, food, rent, whatever) Plant the financial angle on her in a dignified way if she seems amenable to a little guilt or pity for you.
Be strong, boys. And remember all the things you can buy once you hock the ring.