Only the person named on each individual ticket will get miles for travel (they do not all go to the primary traveler). This means that your wife and each kid must each have their own Skymiles account. Many of the benefits of the Amex card only apply if the primary cardholder is flying on the reservation. Your wife would need to have her own DL Amex card and account (not just an additional card under your account) in order to get the benefits of the DL Amex card such as priority boarding and free first checked bag.