Driving without a license is a "criminal law" issue. Trying posting the question that way. Since in most states driving without a license is a misdemeanor it will come up when you apply for green card and should be dealt with now while you can present a defense, if any, to the court. By the way, if you overstayed your visa waiver 90 day stay you should talk to an immigration lawyer as soon as possible. Also your wife should apply for naturalization as soon as she is eligible.
You may also want to do a little bit of research on whether UK has a treaty with US for UK citizen driving in US. Mexico has some kind of treaty with US. Details should be checked on the treaty and your local state law on this issue.