Itinerary spain!

This still feels too hectic to me. Aside from the issue of trying to visit five sight-rich cities in only nine full days (plus some hours on the arrival day), I'm concerned that you have either an early departure or a late arrival on four of those days. I could see trying that pace for a long weekend (though I wouldn't choose to do it), but you're going to be in full-rush mode for nine days. You'll never be able to settle in anywhere. It's just not my idea of a pleasant vacation.

What time are you going to have to wake up to get to the airport for that 7:50 AM flight to Granada--4:30 AM? Are you aware that in Spain dinner begins at 9 or 10 PM?

With only ten nights I would probably leave Barcelona for another trip. However, if your intent is to ‘see it all’, then I would definitely add a night to Granada. And ditch the early morning starts ... you are on holidays.

Sunday, August 26th 9:25 AM
Arrive in Barcelona (3nts)

Monday, August 27th
Barcelona

Tuesday, August 28th
Barcelona

Wednesday, August 29th
Fly to Granada (2nts)

Thursday, August 30th
Alhambra

Friday, August 31st
Train to Seville (2nts)

Saturday, September 1st
Seville

Sunday, September 2nd
Train via stop in Córdoba to Madrid (3nts)

Monday, September 3rd
Madrid

Tuesday, September 4th
Day trip to Toledo

Wednesday, September 5th 10:55 AM
Depart Madrid for New York City

Trains/planes I would be looking at ...

Vueling VY2020 (Aug 29)
Dep 10:30 BARCELONA
Arr 12:00 GRANADA

TRN13941 (Aug 31)
Dep 08:43 GRANADA
Arr 12:07 SEVILLA-SANTA JUSTA

AVN 8095 (Sep 2)
Dep 09:20 SEVILLA-SANTA JUSTA
Arr 10:05 CORDOBA-CENTRAL

AVE 2361 (Sep 2)
Dep 17:00 CORDOBA-CENTRAL
Arr 18:54 MADRID-PUERTA DE ATOCHA

When traveling by train, one can only reach Toledo from Madrid; it's on a dead-end rail line. It would certainly be convenient if one could stop there between Madrid and Seville or Madrid and Cordoba, but it is not possible.

Personally, I think you are trying to do way too much with too little time - you will be spending more time in transit than you would seeing any of the places you've listed on your itinerary.
So, having said that, my recommendation would be to either:

1. Just do Madrid and Barcelona with Toledo and possibly Segovia as day trips.
2. Drop Barcelona altogether and just do Madrid, Grenada and Seville.