I'm not going to tell my wife a secret I promised someone I would keep.
Do you think your wife needs to know this secret that you won't tell her about it?
It's a secret I promised to keep for another person. She has no right to know.
You don't have to tell her. You should keep your promises and not tell secrets.
If I don't tell her, it will cause trouble. I don't mind the trouble I'll be in.
I feel like you're conflicted whether you should tell the secret or not. If someone's life is in danger or will be harmed because of this secret, then it is expected that you tell the secret to your wife. If no one is in immediate danger, you should still keep your promise and not tell anyone, as the person who told you must have really trusted you with it.