Fly into Madrid, drive to Barcelona and drive the coast

I think you need to decide which places you want to visit.

12 days is not long, when the drive to Barcelona will be about 7 hours, and the total driving time from there to Gib would be about 13 hours.
In my view, Gib is not worth the trip.
Consider using trains to take in two or three of Granada, Cordoba, Seville.

It's not yet clear. For Madrid and Barcelona, it depends on how many days you wish to allot to those. It would not be unusual to spend 6 days in each and travel by train. If you want to include Majorca, then I would fly in between and only rent a car while on the island. If you want to add one more destination and spend fewer days in the cities, Zaragoza is on the train route and very appealing (I had it slated for a trip that was cancelled).
So, I would determine your plans for the cities and then decide. It's a a bit like Italy in that you want to use train for the cities and rent a car only for rural village/small town travel. There are some appealing places for car travel in those areas, but some are rather far apart so you'll have to choose carefully. I visited Cuenca by car from Madrid and enjoyed in very much.

My opinion?

Look at picking up the car in Barcelona, then dropping off somewhere before returning to Madrid (Seville maybe?) this would save you a few days as well as driving in the Barcelona area and the drive to Barcelona.

Skip Majorca, or the drive up the coast, doing both does not work.

Plot out where you want to go on the coast, Valencia, Alicante, Almeria, some smaller towns, Malaga, are all on the coast and on the way to Gibraltar. There are also many non-descript resort towns with no "Spanish Charm" and the accompanying crowds.

For 8 nights, you are looking at maybe 4 stops with a car, with maybe 4 hours of driving between stops.

Lorie,
I agree with the others;
decide where you want to go as you may not need a car.
Spain has a great railway & bus system with multiple trains (and buses) including high speed trains to get you to most cities.

If you decide to visit Andalusia, keep in mind that the weather will still be hot in September.

Happy planning!

Driving from Madrid to Barcelona (6-1/2 to 7 hours, probably, if all goes well) is not a good idea when the fastest trains make the trip in less than 3 hours.

The most historic (I would also say the most interesting) cities in southern Spain are not on the coast. There's a reason why Seville, Cordoba and Granada have been major destinations for centuries. There are definitely worthwhile coastal stops, but for me even Malaga and Cadiz would be much lower priorities than the first three. On a twelve-year-old trip, it's not easy to find time for secondary destinations if you want to fly into and out of Madrid and see both Barcelona and Andalucia.

Take a look at a good guidebook and make a list of what you want to do at each destination. That will help you figure out how many days to plan at each stop. That varies from traveler to traveler. Art lovers will spend close to two days just in Madrid's major art museums.

If you want time for off-the-beaten path places, I'd consider reducing the geographical area you cover.

Driving down the coast would be very slow travel. Do a mapquest or use your google maps to see how long it would take to drive from Barcelona to
Gibraltar. Frankly, I would never want to do that.

We drove to Gibraltar from Ronda (daytrip, not overnight), and I'm not sure it was worth it.