Should I let my wife move on...?

Cause-Effect due to your wrong doings. Although we should endorce putting a broken relationship back, I cannot see good things ahead in this relationship. Sad, people do not realize that an affair or criticizing thier spouse could cause harm, they still insist in banging their head against the wall. You first have to be prepared for a lasting commitment and then get married. If I am mistaken and you still can repair this desaster, go ahead, be a man, and get your family back!