Calmly tell your wife "I'm surprised that you would doubt my loyalty to you. If I wanted to cheat on you, I would go out of my way to hide things from you. Instead....from the very beginning.....I have been very open with you about my coworker. I've told you who she is and what she does. And even when you saw her picture on my facebook account.....I never attempted to lie to you about her identity. Instead I confidently and truthfully told you who she was......because I have no guilty conscience and I have nothing to hide. Similarly, I have hidden nothing from this coworker about myself. She knows I'm married and that I have a child. Keep in mind that I work with her. If I remove her off my Facebook list.......things can get awkward at work. A marriage is supposed to based on mutual trust....especially if your spouse is being very open with you and is hiding nothing. Please reflect over what I've said. I'm hoping that our relationship is not that weak that a mere picture of some woman i"ve already told you about can shake it up."
Say this to her calmly. And let her reflect over the situation and her response.