“While we are free to choose our actions, we are not free to choose the consequences of our actions” – Stephen R. Covey
It's important to realize the only person you have control over is yourself. Therefore it's up to the wife to forgive and accept things in her own time. You don't want to be pushy or come off impatient over an issue you created. All you can do is apologize sincerely and state what you intend to do in order to make sure nothing like this ever happens again. Let her know you love her with all of your heart and you understand she will need time to decide if can she deal with this situation. Tell her whenever she is ready to talk about it you will be waiting.
Afterwards you put your focus on taking care of your home, providing for your family, and looking for ways to the lives of everyone in the house. Never be pushy about getting forgiveness. Remember your actions created this mess. You have to be patient and accept whatever decision she makes and learn from it.