Origin is amm. They are wrong and but they can do anything they want.
there is a rule that you cant backtrack to the country of origin.
probably their logic is that since you can end the RTW anywhere in the middle east. they define the DOH as the same country as AMM.

you can try to argue with them or you may try to find a different route.

if she is fine with hkg doh cpt doh. then it is just anything. the ticket is owned by AA and i doubt any other airline would be happy to take over it. so. u have no choice but to follow AA instruction.

try hkg lhr cpt doh or something,