Itinerary advise for Andalucia during Holy Week

With only seven nights and a desire to see a bit of both Andalucia and Madrid, you cannot afford to split your time in Madrid. You need to head out of Madrid the day you arrive so you don't waste time checking in and out of a Madrid hotel twice. The easiest thing to do is to go to Cordoba on your arrival day. That's your closest destination other than Madrid, so the cost of buying a same-day train ticket won't be as bad. However, Spain is the rare European country where trains sell out with some regularity. I'm not sure it's safe to count on being able to buy a well-timed ticket for the trip to Cordoba after you get off the plane in Madrid. You might need to buy those tickets ahead of time, leaving a decent time buffer to get off the plane and through the immigration procedures. Although you can pay a bit extra for tickets that are changeable, I imagine that would work only if there were still seats available on the trains you wanted to change to. I hope another poster here can say for sure.

Two nights in Seville would be really, really short even if you weren't traveling during Holy Week. Although nearly all sights will be open, there are likely to be some operating-hour adjustments that week, and it's true that the processions will slow your walks around the city. Personally, I'd limit Madrid to one night on this trip and give Seville three nights, but that's just my preference. If yours is a group of big-time art lovers who want to hit the major art museums in Madrid, you'll need more time in Madrid, which means dropping at one of your other destinations--and dropping the one night in Cordoba might be insufficient.

You really need more time for this itinerary.

Things you need to do immediately:

• Check on tickets for the Alhambra. There are still tickets available for April, but nearly every day that month has limited availability. The Alhambra is a large complex where a lot of people spend more than half a day. Tickets are timed, and you don't want to be stuck with a late entry time. The basic "Alhambra General" ticket is probably the one you want. Do not buy the "Gardens, Generalife and Alcazaba ticket, which doesn't include the Nasrid Palaces, which are the prime sight at the Alhambra. Alhambra -- official ticketing website

• Book your hotel in Seville. Holy Week is an extremely busy week in that city. You may run into a minimum-stay requirement and a stricter-than-usual cancellation policy. Lodging rates are likely to be at least twice the average during Holy Week, and the situation will probably get worse if you delay.

You don't need to worry about this now, but there will be long ticket-buying lines at the Alcazar and the Cathedral in Seville. You'll want to buy tickets for those sights (assuming you want to see them) online before arriving in the city.

Thank you @acraven for your detailed reply. So adjusting our time as follows -

April 16 - Arrive Madrid, train to Cordoba (1 night)
April 17 - Train to Granada (2 nights)
April 18 - Alhambra visit
April 19 - Train to Seville (3 nights)
April 22 - Train to Madrid (1 night before flight back home)

Would moving the Seville portion to the end (since Holy week ends April 20) allow for a more relaxed time there and fewer crowds?

It might. Perhaps one of our other posters can provide better intel on that. Without specialized knowledge, what I'd do is check lodging rates on booking.com. I'd expect them to track the overall busyness of the city, at least to some degree.

Acraven and Intrepid are approximately right except that it logistically doesn't matter which of the three cities - Seville, Cordoba, Granada - you see first. But check booking dot com and see if hotel availability and prices vary depending on which city you see first and second. My plane arrived in Madrid before 9am; I had an advance train ticket for about 3pm; my first city was Seville, then Granada, then Cordoba, then Madrid. My trip was 13 nights. You might want to add a night to Seville.