In order to quickly visit Cordoba, we'd like to get off the AVE train for a few hours. Do we need to buy tickets for Sevilla to Cordoba, and then separate tickets from Cordoba to Madrid? In other words, are AVE train tickets time specific? Thanks!
Yes, AVE trains are time and seat specific.
I have found the "local" trains to be much less expensive and I can't tell the difference in accommodations. The difference in the travel time is negligible. I would buy a ticket to Cordoba, then buy a ticket on the train you want to Madrid from there when you are ready to leave. Seeing the Mezquita and the Jewish Quarter are well worth a few hours; it's good that you aren't rushing through Spain!! If you are so lucky to be old enough, the "Tarjeta Dorada" gold pass for seniors saves a lot of money on train fares and costs only 5 Euros.