Personally I don't recommend trying to see so much of Spain, which is a really big country, in only two weeks. I would recommend focusing on 2-3 major cities with smaller stops and daytrips in between.
But to answer your question directly, the easy answer is to drop a couple days from Sevilla. I love Sevilla but 6 nights is a lot. Plus Cordoba, which is worth an overnight, can easily be a stop between Madrid and Sevilla. You can check bags at the bus station across the street from the train station. Allow about 4 hours to see the Mezquita, more if you want to explore more of the city and have a meal.
You may also need an extra night in Granada. It's a 3 hour trip from Sevilla plus time to transit and check into a hotel etc... Then catching a flight the next day. That leaves a pretty short window to see the Alhambra, which is a half day itself.
You'll want at least an extra night or two in Barcelona, especially since that first day is limited with arrival, check-in and jetlag. Even day two you might be dragging by afternoon.
You may also find that you reduce your daytrips. That's the nice thing about daytrips: you aren't committed to them and if the weather is bad or you are too tired or just realized that you have overscheduled, you can skip it.
