@LondonElle
I have to say I agree with the posters saying this is not a good sign. I don't think I would have married my DH if he had ordered me not to invite my cousin's partner who he had not met. Because I would have seen it as a warning that he was controlling.
When I got married, my brother's new G/F of 6 weeks came, and I had never met her before. Also, several mates of mine came and I had never met their boyfriends before either. It happens at weddings! I know a few people who have got married, and had 150 people there, and not ever met as many as 2 DOZEN of them - old family friends of their parents, partners of people they know from work etc..... As I said, it is not uncommon to have a few people at your wedding who you have never met.
This bride sounds fucking awful. As has been said, she is going to be a nightmare to be married to! Fuck that. If I was your cousin, I would run for the hills NOW, and not look back!
And why do people keep saying 'it's HER wedding?!' It's the groom's wedding too! 
And he is 'working behind the scenes to sort it!' What the ACTUAL fuck?! 
Oh and yeah, DECLINE the invitation. And yes, make sure the family know why.