It was a gift. It's yours, and you would be justified in keeping it.
That said, if you do not want it and have no use for it, it's absolutely worth being the "bigger person" and taking the high moral ground of returning it. Messaging, calling, or otherwise letting the mother know that the ring is on its way would be appropriate. It does not require a long, involved explanation or anything else that may stir up emotion or drama. Something as easy as stating "I am returning the ring, where and how would you like it sent?" would suffice.
Based on what you said about the mother, I would not expect any overt gratitude or effusive thanks in return. That's okay; do this for your own sense of well-being, not hers.