Is this what you want long-term, OP? To be with a woman who will not "allow" you to do reasonable, normal things because of her own insecurity? This may be the first big dilemma, but it will not be the last, I promise you.

The thing is - this is HER insecurity and she's making it YOUR problem. You can't take that on. You have to tell her, lovingly and kindly, that you want to be in your good friend's wedding, you are sorry she doesn't trust you, but you've given her no reason not to, and if she won't accept your decision, then she should break up with you. And then remind her that going to the wedding is your decision, what she does in response is her decision, but you'd hate to see her throw away a relationship over something silly like this.

And when she doesn't break up with you, because she probably won't, do NOT let her throw this in your face. Any time it comes up, shut it down immediately. "I am not going to discuss it. It is irrelevant and a means of manipulation. Please stop bringing it up or I will walk away from this conversation." And if she does break up with you? Then, as sad as you may feel about it, you will have dodged a major bullet, because anyone who would drive a wedge between you and a good friend, deprive you of a fun wedding weekend, and all because you had a relationship with someone BEFORE YOU EVEN MET HER, is crazy as shit. Your life will be misery if you let her get away with this.