God Bless you for your dedication to your important role in his life as sponsor! As a Confirmation Catechist at my home parish I am delighted to see this role taken seriously.
Please know that your moral obligation to be an exemplary Catholic IS best served by NOT “nagging” him. You are fulfilling, not shirking, your duty in following the above advice. He has responded with hostility. The next time will not go better. Communication is about more than sending the message - it is about the receipt. If you “nag”, he will be strengthened in his misguided belief that God and the church want nothing more to do with him, and that Catholics are rules-oriented robots. Now of course we know that’s not true, but the goal is for him to know it!
Think, brother, how Christ approached us. When we were dead in sin, He could righteously have pointed out all the many ways we fail Him each day. But he did not… He came gently, peacefully, as a baby, LIVED His example, loved and served.
THIS is the way to your wayward cousin’s heart… love him, serve him, do not shun him (did not our Lord Himself eat dinner with sexual sinners - prostitutes? How many prostitutes would have stayed near Him if He spent the time pointing out all their flaws? No, friend, He let people be drawn in by His light and love, and then, when near enough, He lead by example).
Prayers to you that you will have the strength to do the same!