Is my cousin wrong to ask for an invitation to my wedding?

Asking people for an invitation to their wedding is rude because it puts people into an awkward position. If they wanted you to attend, they'd have asked you to attend. They didn't. The impulse to make them refuse you to your face is an ugly impulse and should be resisted. 

There is nothing wrong with asking for what you want.  Often you don't get what you want unless you DO ask.

But just because someone asks doesn't mean you have to agree, nor feel bad if you don't comply.

What COULD be wrong would be for the cousin to throw an emotional scene if you didn't grant them their request.

There is no wrong or right about it. She can ask anything she likes, just as you can answer in any manner you like.