What's the best way to spend two weeks in Spain?

Howdy,
Four nights in Seville will allow a good relaxed space. Use train bus to daytrip to cordoba. From seville to ronda for a night can suffice, then drive to Granada (personally believe three nights suffices) then fly to barcelona. We greatly enjoy driving throughout andalusia due to relaxed pace of just seeing what we can find off the beaten path. Using a car rental just to get from point A to B may not be the best option given how good public transportation via bus/train is throughout Spain. Example: with four folks, plus luggage, you will need a larger car. Parking, fuel, securing valuables can all add to travel stress. If you do rent be sure and obtain the required international drivers permit, $20 at AAA. Please doitch the car upon arrival in Granada as almost a guaranteed ticket attempting to drive in old town. Also reserve your alhambra tickets now!
Suggest you review Airbnb to determine if renting an apt offers better options for ya'll. We seek to rent apts first w fallback being a hotel. Apts offer more space, kitchen, better financial deal and often a landlord who doubles as your own information center. If possible seek apts w terraces as very nice to kick back in the evening w sangria, cheese and jamon. Be sure and request apts w A/C.
Fyi: it is also possible to day trip to ronda from seville.

I think your itinerary is perfect. The first decision is north or south and you've made a good choice, especially for the time you will be there.

April fair in Seville is May 6th to 11th this year. It comes a set number of days after Easter, since Easter is late, so is the April Fair. During the fair you have the opportunity to visit the fair grounds for a true cultural experience. Make sure you plan some of your time around the fair. The fair starts at midnight and runs 24 hours, plan on a day visit to see the horses and carriages and a night visit for the parties. The traditional clothes are impressive (notice the girls have a zippered pocket, that acts as their purse, in the ruffles of their dresses). A few trips to the fair and polka-dot flamenco dresses start to make sense.

If you want, they also have bullfights every night during the fair. It's not for everyone, spoiler alert - the bulls die after being bullied by toreadors, picadors and the matador (sometimes the bull will maim a person or horse in the process). I was glad to see one, because it's a cultural experience in it's own right, but I'm not sure I'd recommend it without knowing the person I'm recommending it to.

Seville's Alcazar and Cathedral (where Columbus is entombed) are both must-sees. I'd also plan one evening at a Flamenco dance performance (try to find one with more than just one guitar player and one dancer).

Ronda is a nice intermediate stop, one night is probably all you need. I liked the stairway down to the bottom of the gorge. If you skipped the bullfight, you can visit the museum at the bullring.

Granada is another truly great stop. The Alhambra is probably one of the world's top sights. They don't talk up the Arab baths in the Alhambra. If you haven't seen baths elsewhere, however, find them and have a look. The view from Albayzin is another to put on the list, especially if you're into taking pics. The Albayzin also offers cave homes with Sambra dances; I'd give these a try. You can compare and contrast to the Flamenco performance you saw in Seville.

Cordoba is easily reached by fast train from Seville. I'd be tempted to visit Granada first and end in Seville so you can stop in Cordoba, then just continue on the fast train to Barcelona. Plan a minimum of four hours to see the Mesquita and surrounding quarter, take a taxi to and from the train station to maximize your time.

Granada to Barcelona is a tough trip because there aren't any convenient options. Plane is probably the best if you aren't planning intermediate stops. Rentals work fine as do buses, the driving in Spain is easy and the roads are in good shape. I avoid the AP roads in favor of A roads, N roads would be my next choice. Driving that particular leg, however, wouldn't be my first choice because it's such a long way (9 1/2 hours driving time alone, with no stops).