Thanks for all the advice. I suppose I could bring an ordinary copy of the marriage certificate just in case, but I don't want to spend $29 and wait a month for the county to send a certified copy. And nobody says that's a requirement.
I do have the wife's birth certificate (again, not an extra certified copy...just an ordinary copy), but I'm not sure what that proves.
Perhaps I'm overthinking it, but the system just seems a little broken to me without verifying the chain of names for each parent present at the appointment. If the issue is parental consent, and the official accepting the application says "same first name and DOB, good enough for me!", I suppose a guy who had a kid with JANE DOE born 1/1/1990 could find a woman named JANE ROE who also happens to be born 1/1/1990, and bring one JANE ROE to the passport acceptance appointment. The official has no way to know whether one Jane Roe is the mother who changed her name -- or an entirely different person.
(By the way, this reminds me the stories where someone breaks up with a significant other and tries to find someone of the same name to go on a planned vacation so they can use the plane ticket.)