Having children is always a big concern when it comes to making this decision. If this was her first time, and she really wants to make it work then forgiveness can happen. This is a choice only he can make, while everyone can give him different opinions at the end of the day he must decide wither he wants to forgive her or not.
Everyone makes mistakes, and cheating is a common one. The fact is it is far easier to cheat then most people know. What starts off as a innocent flirting can get out of hand quickly and often even though the women had no intention of cheating she can find herself in that position before she has really given much thought to it. Of course that does not make it right, but it is something he may want to consider when deciding on what to do.
The fact that they have children together is a serious concern, a split would cause damage to the family unit. While kids do learn to adapt well the fact is if this was a one time mistake then it is something he may want to consider forgiving her for.
Now with that being said, I would strongly urge him to seek counselling on this matter. Before deciding on wither he will forgive her or not he should first set up marriage counseling so a counselor can help them deal with the betrayal and learn how it happened in the first place. This will give them both a chance to address all the problems in the marriage including this one. They will learn how to communicate better and how to learn to forgive each other.
The fact is everyone makes mistakes, but if they love each other and both are willing to work this out then yes he can forgive her and learn how to have a stronger marriage.
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