I twice previously started to post again to this thread but deleted my comments before submitting them as I was not sure my thoughts at the time would have been constructive in any way.
What I will say now is that it would take a very special man, in particular, to get over this. Only you know how you feel, whether your wife is capabale of remorse & undertaking a commitment never to do the same again and also whether your staying togther would be better in your situation for your child or not.
One thing that occurs to me is that without removing the cause, as stated by you, i.e. your long absences and her wanting to work weekends, surely there is a risk of this happening again. I further suspect that you saw the signs before the present outcome manifested. If so, was there no way to head this off? It's not in anyway meant as any form of criticism but rather a genuine question.
Good luck to you!