In contrast, close as my girls and I are, they don’t look at jewelry as a reminder of me. They aren’t vested sentimentally in those items, in that way. Other things, yes.
It’s a tough reality that she had no connection to that grandmother. But I’m not convinced she would crumble.
Some may indeed be projecting. It’s kind that you care about her possible feelings. But it may not be necessary. Not to this extent, for this item.
The best approach in this sensitive and emotional situation is an old fashion written letter. This letter can be drafted/rewritten/edited and proofread by all. You get it written just like you want it. Have all the beneficiaries/cousins sign it. There would be no mix up of words, remarks, awkwardness, etc…
You can present this gift along with the letter. I would personally request her to open the letter and gift at her home away from everyone.
I’d focus on it being the MIL’s ring, not the grandmother’s. You can tell her the history, but that the MIL really loved her (and her mother) and wanted her (cousin) to have something from the family. Make sure she knows she can do anything she wants with it as will all husband’s sisters/daughters with their pieces.
I agree with the OP and the rest about offering the ring. I would not say anything about the “value” of the ring. Is it is appraised, based on replacement value, for $50k, you might only be able to sell it, used, for $25k and then would pay 30-50% to the seller, so might receive 12-15k net. Jewelry can be tough to sell and tough to net the value perceived by the deceased owner. Ask me how I know 
That doesn’t make it any less gorgeous.
Perhaps tell her you’d like to offer her the ring and have it be all about your MIL, who missed her sister so, and nothing about the grandmother.
I have a different take on your question and wanted to share it with you just in case your cousin might feel this way.
I could see someone not expecting to get anything from your mom’s estate, but yet when the offer of the ring is made, getting offended. Why are you making this offer? If it is to right your grandmother’s wrong (in disinheriting your aunt), isn’t the proper way to rectify this to figure out whatever half of your grandmother’s estate was and give that half to your cousin (I assume your aunt already died)? I could see feeling like anything less than that is just a token.
I happen to come from 2 generations of people being disinherited or threatened to be disinherited due to marrying outside of their ethnicity/religion. My parents and grandparents accepted this as the result of their conscious decision to go against their parents’ values. They were proud that they stood on their own, and stood up against this bigotry and prejudice. They felt like they got something better than an inheritance, they got the ability to live their lives the way they wanted and they refused to be constrained by small minded individuals.
So, given my family background, I wouldn’t offer anything from grandma’s estate. What happened between grandma and your aunt was between them. Instead of revisiting their choices, I would offer something from mom’s estate to reflect the love and affection that my mom had for her sister, and the love and affection you have for your cousin.
Personally I think it’s a little odd that the focus is on the grandmother’s ring at all, given that’s the person who was the source of the rift and someone the cousin never met.
Have you considered offering something from your MIL instead? Either a piece of her own jewelry or something else? After all, your MIL is the one who snuck out and supported her sister, and later her niece. I would think that something from your MIL would have much more emotional significance than something from the grandmother.
As for the grandmother’s ring - unless you all have fond memories of grandma, how about selling it and using the proceeds for a broader family reunion in a post-covid destination vacation spot? Generate some good memories from a reminder of a bad one. Sort of a “poke in the eye to grandma” bit of turnabout humor that the cousin might appreciate.
I had family issues, too. Not as severe, but hurtful. It did take a long while, but I like to think I grew up past all that, that I came to control my life not that one of the realities controls me.
And not that, decades later, other family are still clinging to this, in our relationships. (“Oh Poor Dear. She can’t possibly have a life…”)
But OP described the cousin as, (let’s call it,) successful.
I think you have to decide, which is it?
I would have resented anyone taking away my right to decide. And, on the basis of, WE thought you might react badly. (Been there.)
Maybe this ring is the wrong token, after all. We don’t know alternatives from MIL’s things. Seems clear she wasn’t included in the will or not this particular ring. But I wouldn’t want to have it offered with the caveat that I might not want it or the certainty it would crush her.
Very interesting take. Appreciate it. Do note that my MiL was the opposite of her mother. Not ostentatious at all. She owned no jewelry of her own (unless you count $5.99 stuff from TJ Maxx. Lol). She had the money to buy this stuff but had no interest. Her mother’s ring and some other valuable Jewlery were in a safe deposit box and never touched. Much of the grandmothers jewelry is pricy but super ugly. The ring though is gorgeous. That’s why we thought of offfering that. Everything but the jewelry was in trust ( my husband and his sisters shares are actually going to our kids and nephews/nieces).
I like @anomanda’s idea - sell the valuable jewelry and take a memorable extended family trip as your MIL’s treat. It wasn’t mentioned, but it seems this cousin was an only child, right?
Don’t sell the jewelry. The cousin probably has moved past the idiocy of the racist grandmother, and it sounds as if she surely doesn’t need any money from her aunt’s estate, and perhaps your children and nieces do.
I think that a Dear Cousin letter is in order, explaining that there is valuable jewelry from your mother’s estate, inherited from her mother. That you would like to offer her all the jewelry, if she would like it. (What she does with it afterwards is her affair - she may flush it down the toilet, if that’s what she wants). And that if she doesn’t want it, that you propose that you sell it all, and use it to pay for a wonderful family vacation together, all of your husband’s sibs and their spouses and children, plus his cousin and her husband and daughter, whatever the amount of money will buy, for after the pandemic is over. In my opinion, that use of the jewelry would probably have made your MIL very happy, and it is the ultimate “living well is the best revenge” response to your husband’s grandmother’s monstrous behavior.
Does the cousin know about the ring?
I don’t feel at all the same way others do. I’ve seen what rifts can do in families and I’ve seen families later come together after those who have caused the rifts have passed away. The cousin doesn’t seem to hold any grudge against you and she didn’t have any grudge against your MIL. The ring became your MILs when the grandmother died. It may not matter that it was once owned by the grandmother and your cousin may be touched that you thought of her at all.
I would simply say you wanted her to have something from the family. The value is irrelevant since she has money, and it sounds like she has class, something the grandmother didn’t have. Just tell her it was passed down in the family and you feel it should rightfully belong to her. That it doesn’t make up for any of the pain it may have caused in her family but you thought she should have a piece of the family. If she doesn’t want to keep it in her family, you all understand and in that case maybe she can do some good with it, sell it and donate it to people less fortunate than her. Or if she refuses it from you, that’s what you should do. Sell it and donate the proceeds perhaps to some charity involving racial injustice since that is how this rift in the family started.
I would say something simple such as ’ your aunt / grandmother (not sure of the relationship?) wanted you to have this ring’ I’d keep it simple, thereby avoiding any potential for offense.
I think the basic idea is to allow them, finally, to have a say in things. And when dealing with potentially upsetting topics , shorter is better.
I think a phone call might be better than a letter. And why not just be honest : " We didn’t know if you would want this, even if it were just to sell it and donate the money, or not. So it is up to you, and we will hang on to it until you know what you’d prefer"
If it were me, I would want the chance to decide. I would also recognize the offer as meant in the best of ways.