You're correct; what your cousins are doing is wrong -- not only in your eyes, but also in the eyes of God. It hurts them, as well, for no one wants to be the friend of someone who will talk about them behind their back. The Bible says, "A perverse man stirs up dissension, and a gossip separates close friends" (Proverb 16:28).
Why is it wrong to tear others down and gossip about them? One reason is because it's usually based on half-truths, or even outright lies. The Bible is blunt: "The Lord detests lying lips, but he delights in men who are truthful" (Proverbs 12:22). But it's also wrong because it's not done out of love, but out of hate. When we tear others down or gossip about them, we are harming them -- but we don't care. We have forgotten the Bible's command: "Love your neighbor as yourself" (James 2:8).
I can't help but wonder why your cousins act this way. I don't know the answer, of course, but I've often found that people who tear others down are simply trying to build themselves up by claiming to be better than anyone else. But they're only deceiving themselves, failing to admit their own sins and their need for God's forgiveness and grace. The Bible says, "Do not think of yourself more highly than you ought" (Romans 12:3).
Pray for your cousins, and ask God also to give you an opportunity to share your concern with them. In addition, ask God to help you not only avoid their sin, but become more like Christ.