Suppose I did buy a couple of tickets consisting of PHX-DFW-ORD ORD-DFW-PHX for travel in one day. What will AA do? Will they deny me the mileage, or cancel the tickets?

I do this type of thing all the time on HP.

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God Bless America West and British Airways

HP - Platinum/975k miles
BA - Dirt/5k Soon to be Gold
NW - Dirt/10k Only using for emergency flights
UA - Dirt/19k miles
AA - 60k/Using to get BAEC Gold and 1/2MM status.