It sounds as if you already have round trip tickets in and out of Madrid, right? I wouldn't want to have separate flight tickets within Spain, because arrival times can't be counted on. It's especially dangerous on the return flight, because if something went wrong with the Granada-Madrid (or Seville-Madrid) flight, you could miss the transatlantic leg and have to buy a very costly one-way ticket home. That's not a risk I'd be willing to take.
You have to be in Madrid the night of Friday, November 25, so you have just seven nights to divvy up. You'll have only six full days of sightseeing time; the arrival day may be nearly worthless due to jetlag and sleep deprivation--or you may be a lot more fortunate than I am. Six days is tight for seeing all of Seville, Granada and Cordoba, I think. If you spend a night in Cordoba (lovely place worth at least two nights), that would pinch you in Seville and Granada. Your idea of sleeping only in Seville and Granada might be the right one. Be aware, though, that it may be cooler in Granada due to altitude; if it's going to be really rainy, you might prefer to tilt more of your time to the cities likely to be warmer.
Rather than day-tripping from Seville to Cordoba, you can save a bit of travel time by taking the above advice to treat Cordoba as a full-day, en-route stop. You'll probably pass through Cordoba every day you change cities, because that's the way the high-speed rail lines are laid out. You can visit Cordoba on the way to your first overnight stop, on the way between Seville and Granada or vice versa, or on the way from your final overnight stop back to Madrid. However, I think it would be really, really dicey to hit Cordoba on your arrival day if you don't plan to spend the night there. I think there's just too great a possibility you'll be too sleepy to know what you're looking at.
Rail service in and out of Granada is much less frequent than service in the direction of Seville, so take a look at the train schedules to see what might work best for getting to Granada. This might be a time to consider the technique recommended by one of our other posters. She likes to begin train journeys later in the day, after most sightseeing attractions are closed. The Spanish rail schedules can be found here: https://www.renfe.com/es/en
Two important warnings:
Tickets to the Alhambra often sell out ahead of time, sometimes far ahead of time. This is the ticket website: https://tickets.alhambra-patronato.es/en/. The ticket-availability calendar is here: https://compratickets.alhambra-patronato.es/reservarEntradas.aspx?opc=142&gid=432&lg=en-GB&ca=0&m=GENERAL. The calendar shows that standard tickets (14 euros) are sold out for Nov. 19 and 20 and availability is limited on Nov. 23 and 24. The somewhat more expensive Dobla de Oro tickets are available for every day of your trip, but in limited quantities. You'll need to buy your Alhambra tickets ASAP; don't wait until you get to Granada (or even to Spain).
It's not uncommon to see sold-out trains between Madrid and Seville on the Renfe website; I assume the same can happen between Seville and Granada and between Granada and Madrid. You may not want to buy your arrival-day tickets now, because who knows when you'll actually be ready to step onto a train at Madrid-Atocha. However, what you must not do is plan to buy those tickets at a staffed counter there. The lines are unbelievably long. The ticket-vending machines have an English option and should be fine, but in the past, some travelers reported having difficulty using US credit cards in them, so there is a small risk there. If you don't buy your tickets ahead of time, you should buy them at the airport train station.
