Is your family big on the meaning of marriage? As in, your gf is just that, some girl you're seeing, until you finally put a ring on her finger. I'm just wondering if this is the reason she wasn't invited, despite you dating her for so long.
Talk to your cousin though. If it's not a slight against your GF, and she's sorry, but had to set limits that she didn't want to go over, then I say go and enjoy yourself. I have a GF and I love her and all that, but, my family is close to me as well, and I can have fun at a family event w/o my girlfriend.