We're not going to get into why you're not inviting given family members. Even those couples who do their utmost to avoid making every single decision still have... This is not about what the other person did to you.
You likely do not ever need to contact someone to tell them they're not invited to your wedding, but if they or another family member ask you about an invitation, we suggest you use straight-forward, un-charged language.
In getting ready for the wedding, focus on the people who you DO know love and support you.
Find friends and family who you can count on and spend some time thinking about how awesome that is.
Yes, it's going to suck, but you can't put it off.
You need to confront the situation quickly and directly.
Generally, this awareness is brief; it's used for a joke or two and then never mentioned again.