OP, I've been to at least two dozen weddings for family and friends over the past decade, and learned quite a few things along the way:
1. R20 is full of shit (and obviously doesn't know much about modern wedding planning). Particularly in this day and age of comparative austerity, the only guests who *must* be included as plus-ones are spouses and/or long-term partners of the bride and/or groom. Only *immediate* family -- meaning parents and siblings, not cousins -- get an exception if so desired. (Incidentally, many single guests - particularly women - don't WANT a plus-one invitation, because if they're single they'll be expected to drag a male friend along, and then spend all night dodging questions/comments like "when are you getting married, dear"? and "that biological clock of yours is ticking away!")
2. OP, this wedding is not about you. Period. Furthermore, unlike many of the queens on this thread, you shouldn't simply jump to conclusions as to why your invite didn't include a plus-one. Most likely it has nothing to do with your orientation and everything to do with the fact that you and the cousin getting married not only aren't close, but also actively dislike one another.
3. I agree, however, with the earlier comments about a black-tie wedding, in Orlando, in August. (I am assuming you received the invite a standard six weeks ahead of time.) Weather-wise that sounds like fucking torture, and I'd turn down the invite on that basis alone. Even more so, I'd avoid it because this type of over-the-top wedding spectacle can only be the product of a bona fide Bridezilla and her absurd notion of a "fairy-tale wedding," or, worse, an idea from her mother. Out of all the weddings I've attended, I've NEVER encountered anyone with the audacity to demand that their guests don true black-tie for a summer wedding in a hot/humid climate, even at several held by the trust-funded families of last names you'd recognize (e.g. Carnegie). Most men don't even own a tux, so they'll have to go out and rent one on top of all the other wedding expenses, and a lot of the women will have to go get something formal, too.
4. Not only is a future bride or groom under no obligation to offer a single person a plus-one, a one-of-10 cousin also has no obligation to attend the wedding, particularly if it involves a significant amount of travel. I've only been to *one* of my seven first cousins' weddings, in fact, and that was only because she lived less than two hours away. Frankly, you sound like more than a bit of a MARY! with these types of histrionics: "if I don't go, I will hear for the rest of my life from my Uncle that I ruined any chance of a relationship with his son. It will all be my fault." Bitch, PLEASE! Once again, IT IS NOT ABOUT YOU, and your uncle is FUCKING RETARDED if he thinks your attendance at the wedding will have any scintilla of an effect on your cousin's future marriage.
Do the sensible thing: send your regrets, and send the couple one of the cheaper items on their registry as a gift.