I would strongly recommend booking all the way through from Dulles to Sevilla via Barajas.
The Metro system in Madrid is quite Byzantine and I think from memory that you would have to change at least once en route to the AVE Station.
One caution though! Barajas Airport is enormous! Three hours should be enough to switch gates etc but be warned.
I have checked the Seville Airport Site and can confirm that Iberia is currently the only operator on the Madrid - Seville route following the demise of a couple of low-costs. Hence the price!
I used the Seville-Barajas route a couple of years ago en route to Johannesburg. All went sweetly both ways.
If you are flying Aer Lingus, you will probably be stopping en route in Dublin. I would suggest that, after a flight to Madrid including a stopover, the last thing you want to do is to have to fight with the Madrid Metro.
For the little extra, fly straight to Seville from Madrid Barajas.
