Should I tell the children about their father's or mother's infidelity?

In general, adult conflicts like this should not be loaded onto children, especially young children who cannot bear it. Telling the story to win sympathy or to make your spouse look bad in the children's eyes hurts them and turns them into weapons. Protect the children's relationship with both parents as far as it is safe. With adult children who already know, speak honestly but without stirring up hatred. Focus on reassuring them that this is not their fault and that your love for them has not changed. If the children are badly affected, a counsellor can help them. Get your own support from adults, not from your children. See counselling.