If the child was from a past relationship, I can't see the issue being a big one. The wife met the man and they fell in love with each other. Perhaps at the start they agreed that the past is the past.
The man is possible embarrassed about having the first child or it might be that he and the mother of the "unknown" child agreed to keep a lid on the child's existence. The agreement predates the marriage.
The now wife obviously found out via another person, someone other than her husband. The husband obviously wants the hidden child to stay hidden because it might cause problems and he was right.
The man is paying for the child. He might accept that the child is his but not want to complicate the child's life who might have another man who the child thinks of as his dad. Adding the real father into the child's life is going to cause confusion, possibly a load of negative emotions. Perhaps now is not the right time.
Bottom line. The wife and husband are together for the hard and easy times, good and bad. The past before they were married is in the past. The past shouldn't be affecting the current marriage because it wasn't a problem at the time of being married.
If the wife feels that she is living a life of deception then perhaps she might quietly ask about the other child and get a few answers.
Could it be that the wife is feeling a bit insecure (all of a sudden) thinking that another woman (and child) might upset her ideal family?...so she wants to run away, just in case it happens.
The past is the past.