Yes, from what you say, your wife probably has become involved with a religious cult -- and one that demands total and absolute obedience from its members. Not all cults are this extreme, but some are, convincing their members to take actions that are clearly contrary to God's will. The Bible warns against false teachers who "follow deceiving spirits and.... forbid people to marry" (1 Timothy 4:1,3).
What can you do? Frankly, it may be difficult to reason with your wife; cults often convince their members that they alone are right, and everyone else is wrong. Logic alone, therefore, may not reach her; she even may have been warned not to listen to anyone who disagrees with the cult's beliefs. Cults also are often led by a strong leader who insists on total obedience, and won't tolerate any disagreement.
What you can do, however, is assure your wife of your deep love for her, and that you are praying she won't be misled into ending your marriage. God gave marriage to us, and it is His will for your wife to listen to Him instead of this group's leader. Urge her to follow Jesus' words concerning marriage: "Therefore what God has joined together, let no one separate" (Mark 10:9).
The most important thing you can do, however, is to pray for your wife, and urge her to put her faith and trust in Jesus Christ. He alone is worthy of our commitment because He alone was God in human flesh, who loves us and gave His life for our salvation.