I'm curious?? Have you spoken to your cousin about your dilemma? Explain to him how much you love him but the struggle you are having inside because of your moral beliefs. Maybe he can give you the permission you need from him to not attend, but at the same time he will know that you love and appreciate him enough to have an honest conversation with him.
Maybe you can invite to take him to a special dinner to "show" your love for him and extending kindness to his "significant other". They both are loved by God, regardless of their sin, and you need to restore and encourage him gently and in love. I don't believe this includes actually attending his wedding.
#308, best answer so far.