Assuming there's nothing more to the SEA-LAX story (your son didn't sneak off onto another SEA-LAX flight (!) for some weird reason, and there aren't any irregularities with payment/accounts):
As distasteful as it is, buy all replacement travel on AA, ideally on the same flights originally booked and ideally with the same credit card. Wait until all travel is complete (so they can't cancel anything else), then submit the claim to AA for the total of any *new* tickets purchased, give them a week, then dispute the *new* tickets with the credit card company. I think you want to present it to the CC company simply: "We purchased ticket <old> on <date>, checked in and started the trip as ticketed. For some reason, AA incorrectly insisted on charging $XXX to continue flying the purchased ticket, which was paid under duress while stranded", or similar.
I wonder if the checkin upgrade wasn't handled properly in their system. Years ago on UA we had a fare drop reticketing the day before our outbound trip; somehow the first agent managed to check us in under the *old* tickets that were effectively refunded, so when we went to check in for the return they claimed we hadn't flow the outbound. Eventually they beileved us and got their central desk to reissue the return tickets, and luckily seats together were still available (we had an infant in paid seat so had to have at least 2 together). Either that or the agents didn't properly scan the BP and got the cross-check count wrong.
Did your son check a bag at SEA? That would be additional evidence that he had flown SEA-LAX ("look, I checked a bag with you in SEA at XX:XX and appeared at the desk in LAX at YY:YY, clearly I flew that segment").