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Although parents may think children are immune to what happens "behind closed doors," they aren't. Children usually sense when something is seriously wrong between their parents, even if mom and dad try to keep their problems a secret. When parents attempt to hide what's really going on, children are left with their keen intuition and active imagination. They intuit that their parents are feeling differently, and they "fill in the blanks" about what might be causing those emotional changes, often blaming themselves.
When infidelity results in a family crisis, I strongly believe that children are entitled to know what happened. Shielding them from the truth only adds to their sense of unease and confusion. With that said, it can be tricky for parents to decide how much they should reveal to a child. Obviously, children don't need to know details of an affair, and what they are told will depend on their age. But children should be informed of the general facts, so that their feelings of confusion and distress can be validated and dealt with. Parents can explain that adults may make serious mistakes, even hurt the people they love.
Children who are told the truth in an age-appropriate way will fare far better than those who discover the secret on their own or are forced to live with unconfirmed suspicions about those they love.