Infidelity likely won’t affect custody issues
As unpleasant as it is to learn, you can anticipate sharing custody with your cheating ex in most scenarios. Although the courts have historically considered cheating parents to be morally unfit, that practice has long since fallen out of favor.
Judges should make custody decisions based on what the children need, which is usually a relationship with both parents even if one has displayed unethical behavior in the past. Only if your spouse somehow endangers your children through their infidelity will it play a role in custody decisions.
Although Virginia does have a law criminalizing adultery, it is rarely enforced. You may need to think about how fighting over this issue could increase what you spend on the divorce and limit your available resources later. Looking to set yourself up for a better future without your cheater may be a better revenge for infidelity than trying to illicit penalties from the courts during your divorce.