North Carolina is a no-fault state when it comes to divorce, so there’s limited effect a supposed affair will have. First, unless she’s the supporting spouse and you are the dependent spouse, it really isn’t supposed to affect alimony. If you are the dependent spouse, then you having an affair could be a bar to you receiving any alimony.
Child custody isn’t supposed to be affected at all by an affair, although if there were proof as to you dating someone potentially dangerous to the child, then it could be an issue.
Despite all this, there are two other issues. First, she’d have to be able to provide good evidence as to any affair. Second, if she “knew” about the “affair” and still continued to live in the same house and have sex with you and the affair didn’t continue beyond that point, then she would’ve been considered to have forgiven the affair and any such affair would be moot.
This is just the quick and dirty explanation.