IIRC, MP VISAs don't offer miles for the annual fee, but you'll find a corresponding mileage deduction from your MP account if you cancel your credit card when the annual fee becomes due and have the fee refunded.

To get back to the original topic: I think having a card signed with Idine for each family member and doing at least one Idine transaction for each (not necessarily all at the same time) should work very well for those who have access to the program.