The value in the ring is sentimental, in its family history. If you're a typical mustachian then in a few short years you're going to have a million dollars and another $10,000 will be a rounding error, an afternoon's worth of market fluctuations. You'll be able to buy a ring just like it and barely notice the cost, but it would never mean as much as this particular ring.
So I would treat it like any other treasured family heirloom, rather than an expensive piece of jewelry. Like a photo album of your grandparent's wedding, maybe, or the journals an ancestor wrote during the war. I'd keep it safe, have a plan to pass it on some day to another caretaker, and not worry so much about how often you physically interact with it. You can certainly wear it any time you like, but personally I wouldn't bother. You don't need to touch something daily in order to value it for sentimental reasons.
We are all caretakers of the things we own. During our tenure as such, we either consume and destroy those things, or we preserve them until such time as they can become someone else's burden. To my ears your story sounds like your mother is finally free of a crushingly weighty obligation, and you're now on the hook to not let her down by losing or damaging it. The best outcome you can hope for is the status quo, and you have a significant chance of ruining it forever before you can be rid of it someday, when you give it away to one of your own relatives. Sounds like a curse, in a way.
So wear it, or don't wear it, I don't think it really matters. The important thing is that you prioritize it's safe keeping forever and forever. Is wearing it daily likely to increase or decrease the chances that you'll lose or damage it somehow? Seems to me like it might be safer locked up in a display at home. Have you considered framing it with pictures of your mother and grandmother, and then bolting that frame to a wall?
