In Michigan, the courts have stuck with a very narrow interpretation of the statutory language, and have not approved a parent's vicarious consent of tape recording of a minor child's telephone calls as creating an exception to the state eavesdropping law. See, e.g., Williams v Williams, 237 Mich. App. 426; 603 N.W.2d 114 (1998). (But you're not asking about Michigan....)
North Carolina takes a less restrictive view of a parent's vicarious consent, as set forth in Kroh v Kroh, 152 N.C. App. 347;567 S.E.2d 760 (2002), observing that other jurisdictions permit vicarious consent:
Quoting Kroh v Kroh (emphasis added)

