Allowing your father in law to assault you is never a good idea. While I am sure as old school he thinks this may be OK, the reality is it is not. This is a issue between you and your wife, and your father in law needs to accept that.
What you did was wrong......you know that already so I will skip the lecture. But keeping this from your wife is even worse. The reality is even if you allow your father in law to issue his own form of justice whats to keep him from telling her later on? And I would question why he felt this type of punishment is appropriate for a adult. If he was truly concerned about his daughters welfare he would have went to her immediately and told her regardless of how he feels about you. While they may be surrogate parents the reality is this is his daughter and therefor his first allegiance is to her.
Something about the whole situation is off and to be honest with you I am concerned. I would advise you to skip right over your father in law and simply go tell your wife what happened. Sit her down and explain to her that you made a mistake and you want to be honest with her.
Your father in law is assuming she will throw you out, and while she may the reality is she may also forgive you. Many women can be forgiving if they feel their partner was honest about the mistake and is willing to work on the marriage.
Let her know why you did this and how you want to ensure it never happens again. Marriage counseling may be something that you would want to suggest so she knows you are serious about fixing this.
In the end you do not want to live with this hanging over your head forever. Even if you allow your father in law to issue his punishment whats to prevent him from using this against you again in the future?
Better to deal with this now, then try to hide it and wind up making it harder for your wife to forgive you in the future.