open jaw spain...sevilla to barcelona.

Joe, it would be easier for us to give you good answers if you limited yourself to one or two related questions at a time. Your plan, what you have mentioned of it, seems feasible, and it's easy to get around in Spain. As for an itinerary, you might want to look first at a few guidebooks to get an idea of what you might like to see in what areas, and determine your timing from that. We can then help you fine tune your trip with better suggestions as to method of travel, etc.

A couple of comments, if I may.
Your first day will be affected by jet lag, so other than a reconnaissance of the city, and a nice dinner, don't plan too much. And your last day will be taken up by your departure from Barcelona. So you really have 11 full days to work with.
Basing yourself out of the three cities is a good idea, but you may be underestimating the distances somewhat. Sevilla-Granada is about 3 hours each way by train or bus....maybe 2 1/2 by car. The Alhambra could be done in a day, but it will be a very long day....and you won't have much time to see anything else. Make sure you book your tickets in advance at www.alhambra-tickets.es .
From Barcelona, Valencia is not a day trip....by car, almost four hours each way...longer by train or bus. Monserrat is a great day trip our of Barcelona.
Travel Sevilla-Madrid-Barcelona is best done by AVE. IF you are sure of your travel dates and times, inexpensive advance tickets can be had at www.renfe.es . They allow purchase 62 days in advance, which is good for us, since their midnight of the 62nd day is actually the late afternoon of the day before, for you.
Since Cordoba is on the train route from Sevilla-Madrid, you may want to consider buying two tickets...leave Sevilla early, stop in Cordoba for a flying visit...then continue on to Madrid.
Travel in Spain is quite easy and comfortable. the AVE trains are very fast, and the highways you'll be on are modern. Top speeds on the freeways are 75 mph...so traffic moves! But they're still nowhere near as fast as the AVE. The only place I might recommend renting a car is from Sevilla, so you have more freedom in visiting Granada, and maybe stopping at Ronda on your way back if you stay overnight.
Even with these suggestions, your trip will still be rushed. I would suggest you cut one day from Barcelona and add it to Sevilla, so you have a chance to really enjoy that city, and have time to overnight in Granada.

I tend to recommend doing less travel on your vacation. When you stack too many cities together you will find yourself completely exhausted at the end of your vacation and you will only remember a blur of sights, sounds, smells, etc. Granada, the Alhambra, Cordoba, Seville, and Barcelona could easily fill up your entire vacation. Your time needs to allow for slow walks down the city pathways, stopping for dinner at a local restaurants, etc. Consider your health and how quickly you are able to rebound from strenuous days. The more healthy the more easy to pack your days with events and sights. The less, then plan accordingly. Plan for down time that is spent doing nothing more than walking about town and getting to know the people. To me I would plan on Seville, Cordoba, & Granada then off to Barcelona by plane. Splitting time between these two regions will increase the probability of getting to know not only the places, but the people also and when you come home feeling like you had a vacation rather than having run a marathon. These are places you want to get lost in because each is unique and full of wonders. Take the time to smell the roses and enjoy.

I returned last Tuesday from Spain. I flew into Barcelona and flew out of Malaga. I spent three nights in Barcelona, then flew to Grenada on Vueling. I bought the cheap airline ticket from their website months in advance. It was quite inexpensive and much quicker than the train or driving. I spent two nights in Granada and spent an afternoon/early evening at the Alhambra with a prepurchased ticket (a must). I then took the train to Seville where I spent four nights. Seville is a convenient city for making side trips, especially to the hilltop villages. Then, I trained to Malaga, changed to a suburban line and went to Torremolino, where I stayed in a very nice, newer, nine room Japanese owned hotel in a residential neighborhood. For two days I walked the ten minutes to the beach, and spent the day relaxing and resting up before flying home.

I did not rent a car, as I am very fond of train travels. None of my trips were on AVE. In Seville, there's a Renfe ticket office not too far from the Cathederal. I fretted about buying the tickets at home but wasn't sure of my schedule, so I didn't, and all worked out fine.

I would highly recommend that you pick up RS or another guidebook such as Cadogan and read up before deciding on your cities. As for me, I like to hang out and enjoy the people and cultures more than covering a lot of territory.

Joe
Maribelsguides.com has some great tips on Spain.
I used her guide to plan my Barcelona and Madrid portion.