I understand the desire to keep it secret, to avoid the public knowledge of your cuckolding and the desire to hide that your wife stepped outside for her sexual needs.
I guess you're a cuckold by definition, but in today's environment, there are lots of totally incorrect associations that go with the term. All it means is that your WS failed as a woman and as a human being. Your W's failure says nothing about you, whether others think it does or not.
In all likelihood, your W DID NOT step outside for her sexual needs. She cheated because she wanted to avoid facing and resolving her own internal emotional issues. In all likelihood, she looked for someone else to cure her emptiness, something she looked to you for, too. The problem is that she's the only one who can cure that emptiness.
Exposing to families is fine if it comes out naturally. Otherwise, it smacks of counting on other people to cure your own pain - but only you can cure your pain.
Worse, if true R is on the table, it might be better to keep knowledge of your W's A more private. Again, seeking support from a family member you love and count to provide emotional support to you makes good sense. If you split, it makes sense to tell friends and family shy you split.
But we no longer place people in stocks so that spectators can through rotten vegies and/or eggs, rocks, and ordure at them.
Look, you're in pain. Exposing one's WS for the purpose of exposing them certainly adds to their pain. The thing is, IMO what counts after being betrayed is reducing one's own pain. Making your WS feel like shit doesn't help if you feel like shit all along.
My reco is to let your W deal with her own shit and her own pain. You'll benefit most by resolving your own.
Part of 'dealing with your own' is, IMO, dealing with the shame of being betrayed. As always, your WS betrayed you only because they betrayed themself first. Feeling shame for your WS's failure makes no sense, but it's something we all (or almost all) have to resolve. And it's your own problem to solve - no one can do it for you.