Seville to Madrid with Day Stop in Cordoba?

It could be choice of departure times and the popularity of these times. Renfe has dynamic pricing (like cheap airlines).
You can check the bus for Seville to Cordoba, but that takes twice as long. The stations are across the street from each other though, so you can store your bag and it will be handy for your trip to Madrid.
The other thing about the Renfe website is I didn't always use the various drop down menus that provided more purchase options.
Some schedules show Preference pricing, others showed Tourista, but when you open the + on the right, there were more options.

What is your age? Discounts are available for over 60.

In addition to the variations from different discount categories, different train types departing, and the number of people who have already taken the cheaper seats on each, it's also usually the case that splitting up a trip costs more than buying a through ticket for the same distance. But at least you're not backtracking to visit Cordoba as a daytrip from Seville.

What website are you looking at? I just plunked in Aug. 8 on Renfe's official site. There are tickets for morning trains Sevilla-Madrid for about €42. Sevilla-Cordoba on the 45 minute fast train for €21, on the slower 1.5 hour train for €12-14. The afternoon/evening trains from Cordoba to Madrid are from €43-55.

Thanks for the tips.

We did look at Renfe and it was showing about 65 euros for the afternoon trip from Cordoba into Madrid. It may be that we have to pay a larger amount to make the stop over.

With four of us, I'm starting to wonder if we should just rent a car for the day.