Her wedding. Not yours. Don't ruin it.
She has to pay for it and it's expensive. Does she even know her cousin's partners? If she doesn't know them well or they aren't a definite life partner, then why should she have them there. Surely your son's can survive one day to celebrate their cousin without needing their partner there. If they don't want to go because of partner, then fine, they can politely decline.
For you to throw a strop and not want to go when they are adults is ridiculous.
It's her celebration, it's perfectly fair for her to not want it to turn into a sea of strangers having their own party.
I invited all cousins in a very large family. This was out of politeness as are important part of life growing up or now, some we hadn't seen in forever or had invites, birthday cards or even a message from forever. However for all family to be together and manners we invited all.
We included partners who we knew and had some kind of interaction with. We also invited partners for cousins who we are very close to, fond of or have been very kind and we appreciate. We invited partners who were likely to become or already felt like family.
Children were all invited because we love them all, they're family and no trouble. We had things in place for guests to make everything more comfortable, whatever that happened to be.
It was noted that if the odd person didn't attend because of the partner whose name no one knew non-invite situation, it wouldn't be the end of the world, so to speak. In other words, polite invite, polite can't make it, can be a respectful no need for drama way of inviting someone you don't especially want there for whatever reason and them not being there and making someone way more important uncomfortable.
In the end no one complained, everyone cared about was there, everyone got along, no one noticed and there was no drama.
At my brother's wedding, one of my SIL's bridesmaid's brought a boyfriend who she wasn't getting on with (neither were pleasant people), he kept interrupting her at the top table were she was sitting and making both sets of parents there uncomfortable. They split up soon after, she shouldn't have brought him. I meanwhile, as sister of the groom, had not been with my partner for a very long time at that point, I was taking care of the children attending, it was huge family thing and I was happy to spend with them all. My brother said bring him to meet everyone or just be there if you want, but it wasn't my day to use an an introduction to hundreds of us whilst I was busy with others and I hadn't been seeing him for a long time, so I didn't. I was sister of the groom, bridesmaid and helped pay for and plan the whole thing. I didn't bring a partner. Again, not always appropriate timing and most of all, not my day!
If anyone had thrown drama like you are, I would uninvited them.