Advice: Should I tell my wife that her cousin has a son for me?

It all started in 2014, when I went to the United States for an executive course, because I am a Senior Manager in an oil company here in Nigeria. I got married to my wife in December 2001 and she has been loving and faithful. A woman any man will give an eye to have.

Though we do not have any child yet, we have not let it bother us, because we believe God's time is the best. My family tried severally to get me another wife, but I refused. 

Back to my course in the United States, where I met my wife's cousin who was living in Atlanta. She flew to Chicago where I was, to get the stuff my wife sent to her and we got talking, so I asked her of her boyfriend because I knew they were having issues.

She was a heavy drinker. When she started telling me what she went through in the relationship, she burst into tears and as I was consoling her, she placed her lips on mine, I felt the warmth of her body close to mine and the rest was history.

Honestly, I felt bad about it and I apologised, and we agreed to keep it from my wife, who we both love dearly. The next thing was for her to call me some weeks later that she missed her period and that she was pregnant for me. 

I told her to abort it but she refused. She stopped calling me and changed all her numbers.

Last week, I got a mail from her telling me she was sick and needed to see me and my wife.

My wife could not make the journey to the US because of her bank job, since I was on my annual leave, I travelled to Atlanta to see her in the hospital. 

She had cancer and she was dying. She then gave me the greatest shocker of my life, as she introduced a 2 year old boy to me as my son. I did not believe her, but she suggested we do a paternity test, since I was in the hospital. 

Behold, when the result came out, I almost fainted. The boy is my son. I told her to give me time to get myself, but she told me that child services might take the boy if she dies.

I told her I heard, and asked her to give me time to think it through, and I left for my hotel, only to be woken up in the middle of the night by a call from the hospital that my wife's cousin was not fine and that she wanted me to come over.

I rushed down there and she handed the boy-my son to me with some documents and gave up the ghost. I have since returned to Nigeria with the boy who my wife thinks is her cousin's son, but I can't tell her anything.

I don't want to hurt her feelings. Should I tell her, how should I go about it?

She will be devastated. Please help me what do I do.

We still don't have any kids yet.