She is correct in that you cannot use the AS codeshare. You would have to either buy a separate ticket or do something such as LAX-ORD-SEA

There is nothing wrong that I can see with your domestic sectors. Obviously you are only permitted 2 stopovers

I would query the benefit of using an agent; personally I would just use the AA ATW desk to book it . If you do use the agent, do make sure that the agent issues it through AA rather than QF to reduce the fuel fines

Dave