An engagement ring is returned if the engagement is broken.
An engagement ring is given well before the marriage as a sign of love and intention to spend a lifetime together.
An engagement ring is not part of marital property unless it's included in a prenuptial agreement.
In the end, stuff is stuff. Ask yourself what the motivation is... a sense of hurt, spite, entitlement?
Many times families will bestow family heirlooms with the marriage... like sterling silver silverware and the like.. whose is it? I'd never sell what's been passed down to me even though the money would be helpful.
Some stuff is just someone else's. And would the fighting and expenditure of negative emotion be worth it in the end?
Choosing what makes one healthier person reaps far more value than opting to fight over stuff.