In reality, you've asked a spiritual question, because God is concerned about everything that concerns us, including our relationships with other people (including difficult ones). The Bible says, "God is with you in everything you do" (Genesis 21:22).
But your question also has a spiritual dimension to it because of what it indicates about your aunt. Her problem isn't simply that she talks too much; her real problem (I suspect) is that she's a very self-centered person, so wrapped up in herself that she isn't concerned about anyone else. Perhaps she's insecure and feels the need to impress others by constantly talking about herself; on the other hand, she may think she's better (and more fascinating) than anyone else. But the Bible says, "Do not think of yourself more highly than you ought, but rather think of yourself with sober judgment" (Romans 12:3).
Whatever the reason, her insensitivity and self-centeredness aren't pleasing to God (which is why this is a spiritual problem). Don't, therefore, think of her only as a problem, but pray for her and ask God to help her seek Christ's forgiveness and new life. Pray, too, that God may give you an opportunity to confront your aunt privately about this; she may not even realize what she's doing.
Ask God also to help you think of practical ways to keep her from being too disruptive. For example, give your aunt tasks to do; seat her with a different group at each meal; set aside times for everyone to share what's going on in their lives.