I appreciate your letter and hope I can offer some perspective.
You most likely cheated on her because the relationship was not fulfilling. You need to be more direct about your disappointments and concerns if the two of you are going to continue. In fact, this will be important in any future relationship. Tell her that her behavior toward you is not acceptable, and that you cheated because you weren’t happy with her. Then be clear about what the lack of happiness with her was about.
You need to develop a clear, strong voice so you don’t have to act out through an affair.
But be prepared to walk away from the relationship if you don’t have an equal partner. Until you have a voice to explain your disappointments, you won’t have a relationship that is balanced. A couples therapist may help. The find help tab at the top of the page will give you information for one in your area.
Couples need time to heal after an affair, but understanding the root cause and healing that is what is most important for the future.