Navigating from Seville to Córdoba to Granada

I have done plan 2, exactly. This worked well. The train departures from Córdoba were ill timed, but the ALSA bus was at a good time and almost as fast as train. Comfortable, etc. Might be even faster than train now if the train track work slows this route. Not sure.
No changes however - get on bus in Córdoba (bus station across from train station, this is also where the lockers are so its handy), get off bus in Granada. Granada bus station is on outskirts so you will need a cab or local bus to your hotel. It's not far or expensive, just take the cab.

In my case (times approximate) it was an 8 AM train Sevilla to Córdoba. Stash stuff in bus station locker and go to mesquita. Lunch, wander the town. 4PM bus out. In to Granada by 7, cab to hotel, dinner at 9 in the Albayzin with Alhambra view to set the mood. 9 is even a little early for dinner in Spain so no problem at all.

Both cities have somewhat limited bus and train schedules to Granada, so the timing that works for you is a key factor. I'd also vote for travel via Cordoba - it's faster and avoids paying for a ticket back to Seville.

Option 2 sounds better mainly because it avoids backtracking to Sevilla.

Have you considered spending an overnight in Córdoba?

Many people visit this amazing city as a day trip, but miss out experiencing the beauty of the city without the crowds.
There's so much more to Córdoba than the Mezquita!

Where will you be before traveling to Sevilla?
If you're flying into Madrid, you could go directly to Córdoba for at least an overnight, then travel to Sevilla.

If your trip is starting in Sevilla, then traveling to Córdoba enroute to Granada makes sense.

We took an ALSA bus from Córdoba to Granada (travel time 2.5 hours).

Bus from/to Granada to/from Sevilla takes 3 hours.

What's your updated itinerary?

Enjoy your trip!

Thanks to all for the replies.

I'm looking at the ALSA bus schedule for Córdoba to Granada. One of the schedules has "ALSA Bus guaranteed" next to it (the others don't). Does this mean the other schedules are "iffy", i.e., they may or may not run? The schedule I want doesn't have that guarantee statement next to it.

Also, we will have our luggage in a locker at the train station. Does the bus pick up at the train station? Or will we need to take our luggage and ourselves elsewhere to catch the bus?

What website are you using to check ALSA schedules?

I presume you will be visiting Córdoba as a day trip from Sevilla, correct?

There's no luggage storage at the train station but at the bus station which is located right across the street from the train station.

Just make sure you arrive at the bus station at least 20-30 minutes prior to your departure so you can claim your luggage & walk down to the bus platforms.
You will need to place your luggage in the bus hold prior to boarding the bus.

It's not a day trip from Seville. We're leaving Seville in the morning, visiting Córdoba, then going to Granada that afternoon/evening.

This is the web site, searching Córdoba to Granada (English version): https://www.alsa.es/en/

ETA: And here's the long link to search showing the "guarantee" trip at 3:30pm: https://www.alsa.es/en/checkout?p_auth=kLLn4lpm&p_p_id=PurchasePortlet_WAR_Alsaportlet&p_p_lifecycle=1&p_p_state=normal&p_p_mode=view&p_p_col_id=column-1&p_p_col_count=3&_PurchasePortlet_WAR_Alsaportlet_javax.portlet.action=searchJourneysAction&originForm=journeySearchForm&_JourneySearchPortlet_WAR_Alsaportlet_code=&serviceType=&accessible=0&originStationNameId=Cordoba&originStationId=2371&destinationStationNameId=Granada&destinationStationId=99084&departureDate=08%2F22%2F2016&returnDate=&travelType=OUTWARD&passengerType-1=1&passengerType-2=0&passengerType-3=0&locationMode=1&regionalZone=&promoCode=&jsonAlsaPassPassenger=

The meaning of "ALSA bus guaranteed" was discussed recently on another web site, and the explanation was that it means the bus will be ALSA-branded. I believe I traveled one time this summer on a third-party bus after buying an ALSA ticket. No big deal.

Over the course of the summer I took many buses in Spain. It wasn't uncommon for buses to leave 5 or 10 minutes late and lose another 10 minutes on the road, but they were otherwise reliable except for the one that did not show up at all. That made for a frustrating day, and a rather costly one since I couldn't get to my prepaid hotel room that night. But that was a Sunday trip between two small towns in Catalunya, Ripoll and Olot, not between two major cities. And it wasn't ALSA, which may well be the largest inter-city bus company in Spain.