I'm going to invite my cousin to my wedding but not his wife.
Why don't you want to invite your cousin's wife?
She doesn't deserve it after all that happened between us since we were kids.
I understand that you and your cousin's wife have some issues since childhood, but it's customary to allow your guests to bring their significant other to your wedding. If you allowing other guests to bring their spouses, you need to invite your cousin's wife also.
Screw her! Look, it's my childhood enemy we're talking about here, not just a random SO I don't like.
Are you willing to tell your cousin outright why his wife is not invited? It's normal to allow them to bring spouses.