I partly agree with Sarah, but she wasn't married. This is a very big difference.
First, get the nephew out of the equation. I don't understand why he's there to begin with, and it even sounds like he didn't do anything wrong. This is about your marriage.
I have 2 friends who went through this. In one case, the marriage survived and it seems to be doing great. In the other, it did not survive. What matters most is that your husband needs to understand he has committed the biggest trust violation one person can do to another. You don't sound stupid, meaning you're too smart to regain your trust in him simply because he promises never to do it again. Also, there's no way cheating can occur without lying, even if it's lying by omission. So he's also been dishonest.
The best "litmus test" of whether or not your spouse fully gets the damage he's done, and he wants to save your marriage, is if he's willing to go to couples counseling. Book the appt when you know he's available. If he does this, there's always hope. If he won't, your marriage is already over. He's indirectly telling you he's not willing to work through what happened, and he doesn't care if you're unhappy. There's nothing to save.