Talk to whoever you need to.
I think part of it is (my wife felt this way) because it’s her body she might feel ashamed, like it’s her fault, and not want anyone making her feel that way. And you know as well as I do that nobody would make her feel that way.
We all know it isn’t, and these things happen. My wife and I also had a miscarriage. Just support her. If you need to talk to someone on your side of the family, do it. Just ask them to respectfully keep it between you two and not bring it up around your wife.
It’s not being sneaky or shady. You need an outlet, too.
Just be there for your wife and support her. As much as you’re grieving, she’s grieving even more. There are a lot more feelings and emotions going on in her head.
Bottom line: It’s ok to talk to a family member you trust to keep it between you two. But ultimately, support your wife. You both need each other to get through this together at the end of the day.