To answer the original question, yes, your relationship can survive.
Someone close to me found out about her DH infidelity. She was beyond devastated, furious and on the verge of leaving.
He was absolutely horrified at her leaving and did all he could to make it work. They had counselling. The counsellor was very hard on him and he took it. She did many things to express her rage. Some of them must have really affected him and only a strong marriage could have survived such emotional wreckage. It went on for a long time. She looked so ill her dd thought she had cancer.
He changed. He was so much more affectionate and careful as a husband. He never ever criticises her in public and they are, I think genuinely happy. This was ten years ago. I was told about six years ago. I couldn't believe it, yet I could.
So yes, but you will take a long time to recover. Your wife does need to be truly remorseful. She needs to take responsibility for her actions. Difficult three year old? Doesn't equate to cheating on your husband. Fine, get help with him but don't let her use that as an excuse.
I hope she will see the enormity of what she has done and then counselling may be helpful.
Ps likely a 22year old may be fitter and stronger than you. No punching.