Let’s suppose you were having an affair.
Your kid discovers you with the “other woman/man”.
Do you attempt to keep the kid quiet with bribes, threats, etc., or do you come clean and tell your spouse?
Well, it depends on how you want to raise the kid. If you want him/her to grow up believing it’s okay to lie/cheat/steal, and that bribes or threats are an acceptable way to circumvent the truth and or law, then I’d say bribe away.
On the other hand, if you want the child to understand that people make mistakes and have to accept the consequences, and furthermore that your family is more important than the other person, you should come clean.
…having said that, I’ll make ONE exception, but it’s a convoluted one.
Assuming that 1) the “kid” is in fact an adult, and 2) you know in your heart that there will never be another occurrence, and 3) you know the child is experienced and capable of understanding that a mistake was made, is regretted and you don’t want to lose your spouse, then
you still shouldn’t use bribes or threats, but you might not have to come clean to the spouse.