You are cheating no wording changes the fact. It’s worse than a one‑night stand because it adds emotional involvement, which hurts a man more than just sex. Some men can sleep with many women and walk away without a second thought. When wome cheat, it’s usually also emotional and ends the relationship.
You need to strengthen the emotional connection with your partner. Both of you must work on it. If she wants the marriage to survive, you must be transparent, or she must be able to see your communications, because your history of lying erodes trust. Change for your family’s sake you have a beautiful family.