Check on the Alhambra tickets RIGHT NOW. If regular (14-euro) tickets aren't available, see about Dobla de oro tickets. If they are also sold out, check with your hotel, and finally consider a tour--but be sure it includes the Nasrid Palaces (there's at least one out there that does not). If you can't get tickets to the Alhambra, I'd skip Granada for now.
People count days differently. You said 6 days, but how many nights do you have on the ground in Spain? Your first day is likely to find you sleep-deprived and jetlagged. Your last day will be occupied with flying back home. So how many real, non-jetlagged, days do you have?
I suspect that when I learn the answer to that question, I'll be urging you to pick two cities rather than three. I don't think trying to see 3 cities in 6 (5? 4?) days is a great way to have a stress-free trip. The AVE trains running from Madrid to Cordoba and on to Seville are very fast. Granada is a bit less convenient to include in a short trip.
I hope you can find affordable flights into Granada and out of Seville, or vice-versa. However, from my origin (Washington DC) I found even Seville far more expensive than Madrid (by something like $500-$600 round-trip). Maybe you will be luckier, or perhaps you can be philosophical about such a fare difference. You have very little time, so it will make quite a difference if you can fly right to and from cities you actually want to visit.