To me the tentative time alloted for both Barcelona and Seville is really tight, and Holy Week activities will probably slow you down significantly in both Seville and Granada. I was in Andalucia during Holy Week this year, and I ran into some issues with early closings, not necessarily publicized in advance. In addition, it was very difficult to move through the center of Seville while processions were going on. I had allowed a lot of time and was able to go with the flow. Being a visitor on a tight schedule would have been terribly frustrating.
Even aside from Holy Week complications, the time you'll want in each city depends on how many of the local attractions you want to visit. You really need to take a look at your guide book and see what sounds appealing to you. If you leave it up to me, I'll have you in Barcelona for seven nights! I'm a big fan of both modernista and Moorish/Mudejar architecture and would rather skip Granada on this trip in order to see more of Barcelona and Seville.
Doing that would probably allow time for at least a day-trip to Cordoba, though that city deserves at least 2 nights; 3 or even 4 would be better. Cordoba lies on the AVE line between Madrid and Seville, so you could travel at least one way by train. Most of the trains from Barcelona to Cordoba take less than 5 hours, generally requiring a change in Madrid.
The train from Seville back to Barcelona can take as little as 5-1/2 hours. I find dealing with airports mid-trip a joyless activity and would choose to take the train.
Alternatively, you could just decide (flights to and from Barcelona notwithstanding) you're going to spend all your time in Andalucía on this trip since it's a great time to be there, weather-wise. You can return to Spain later to see Barcelona, the rest of Catalunya (Girona is great), Madrid and the many great side-trips from the latter. Then on the third trip you can begin tackling the other wonderful destinations in Spain. It is a very large country.