Has my wife discovered I've been unfaithful?

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I am married with two children even though we have not had a formal wedding. In addition to this, I have a girlfriend I have been seeing for two years and she is now expectant with our first child. My wife is sensing that there is another woman in my life but I have not confirmed anything to her. She is now pushing for us to formalize our marriage and is not ready to accept anything other than a church wedding. I am afraid that this may not be very good for my girlfriend who I want to marry as a second wife. She is now threatening to tell everyone including my wife that she is expectant and has vowed to stop any efforts by me to formalize my marriage. Please advice on how I can handle this situation. My wife cannot stomach the thought of there being another wife, I am sure she will just leave me and go. I would not want this to happen. {Samson}