This isn’t an easy issue — but God knows what the best approach will be for your niece, and that’s why the most important thing you can do is to pray for wisdom (and for her). Remember the Bible’s promise: “If any of you lacks wisdom, he should ask God… and it will be given to him” (James 1:5).
However, her reaction to her parents may give you a clue as to the best approach. No doubt they confronted her very directly about her lifestyle, and she has rejected both them and their advice. Perhaps a more gentle approach will get through to her — and will keep the door open for further conversations.
Don’t misunderstand me, however. A gentle approach doesn’t mean you avoid confronting her with her sin or act as if it doesn’t matter. But it does mean you let her know you love her and care what happens to her — and because you care, you’re concerned about what will happen to her if she persists in her sin.
Remind her, too, that God loves her, and He is even more concerned about her than you are. She may resist your appeals — but sin’s wages are harsh, and hopefully when she realizes it she’ll feel free to come to you — and to Christ — for help.