There is more than one issue raised in this last response, and each will take time to deal with thoroughly, so for now, I'm going back to the original question you raised, which is in the title of this thread.
If you haven't already done so, please try and read the whole of Dr Harley's article on
Serial Cheaters. It is a long article packed full of information about different scenarios, but they all boil down to one thing:
For a marriage to succeed after serial cheating, the cheater must want to stop the cheating, because they want the marriage to thrive. In the end, the cheater has to agree to being monitored; they must surrender their independence because they WANT to end their cheating and rebuild their marriage. They must want their marriage far more than they want to continue their life of thrills and conquests.
The article suggests that you cannot imprison a serial cheater into a marriage where they absolutely cannot escape your surveillance. The result would not really be a marriage. Surveillance is necessary, but more is needed for the cheater who has spent years going out of their way to pick up thrills at every opportunity. The cheater needs internally to accept that they are in the grip of the thrill-seeking, and they must want this to stop because they can see how destructive their lifestyle has been.
I can't say whether your wife really feels like this, and I don't think that you can says so, either. Your wife's apparent remorse and sorrow is not a clue to her intentions. The question is: why would you take the chance that someone with her track record is determined to change? Leaving your own child out for a minute, why are you betting on your wife's honesty, when she has been so patently dishonest?
Please read the article and tell me whether you agree with my interpretation of it.