No, you're not just being old-fashioned, but you are facing a dilemma that's unfortunately become increasingly common today. As our society drifts further and further away from the moral and spiritual values it once held, many no longer live according to the standards God has given us in His Word, the Bible.
You have every right, therefore, to uphold the moral standards you believe, even if your niece doesn't agree with them. You also have every right to decide who will be a guest in your home. I know some families might disagree and would take a different path in a situation like this, but don't compromise your own convictions. If you did, your niece might conclude that your moral values aren't as strong as she thought they were.
At the same time, assure your niece of your love for her, and your concern for her future. As you have the opportunity, explain to her that you aren't just being old-fashioned. Instead, you know -- both by experience and by God's Word -- that the kind of relationship she has with her boyfriend seldom lasts, but often brings only heartache and insecurity.
Above all, urge her to turn to Jesus Christ and discover His perfect plan for her life. God made us, and He knows what is best for us. Jesus' promise is true: "I have come that they may have life, and have it to the full" (John 10:10).