Check if Copa issued a different PNR for the AM segments; if so use that one. Otherwise, check here http://aeromexico.com/es/personaliza-tu-viaje/?site=mx that you might need to either select that you purchased the ticket in the US or in a different country. Last option would be to call AM and see if they can locate your reservation with the ticket number if it doesn't come up with the PNR.

If you add your AM number you should earn SkyTeam elite qualifying miles/km for the AM leg, and redeemable miles for the Copa flights.

AM upgrades can be requested by calling Club Premier (not Aeromexico) phone number from 96 hours in advance of the flight for Titanio or 72 hours for Platino subject to availability. If you can't get the upgrade that way or if you have Oro status ask for the upgrade at the airport, preferably at the check-in counter but if you forget to ask for it you can also do this at the Salon Premier desk or at the gate. You'll either get the upgrade instantly or will be put on the waiting list. At least you should be offered to be moved to an AM Plus seat for free either by phone or at the airport.

MEX gate screens show the waiting list for AM-operated flights so you can confirm there that you're on the list.