What makes you feel like you're going to "live with" her infidelity? It's not something you are required to live with OR accept. Your post comes across as defeatist, as though you feel you have no option but to accept it and live with it.

And it does sound like a BS what she says about the affair. She should have been turning to you for comfort through the loss of her father, not another man. And to carry on a whole affair? It's deceptive and sneaky behavior. How could you trust her again? It's possible to forgive and move on, but her reasons for turning to another man in her grief I think point to issues in the marriage that you're potentially ignoring or avoiding dealing with.

If there are issues in the marriage that you're not confronting, it's likely that she will continue the affair or just do it again. I would face whatever is going on straight on. Perhaps get into couples counseling, if you're convinced you want to salvage the marriage.