Do you plan to rent a car or use public transportation? Spain's AVE trains are very fast and will get you from Barcelona to Madrid to Cordoba to Seville much, much faster than you can drive. One problem you'd likely run into by staying out in the country and visiting cities by car is finding and paying for parking. If you just want to visit rural areas (not see cities), that's a different story.
I'm not positive about your timing, but I am guessing you plan to depart from the US/Canada on September 16, arrive in Barcelona on September 17 (a day when at least some of you, perhaps all, will be severely sleep-deprived and jetlagged), and fly back home from Madrid on September 26. That would mean only eight really usable days for sightseeing (September 18 - 25), and I would not try to squeeze in Barcelona, Madrid and the south.
You could easily spend all of your time around Barcelona or around Madrid, taking interesting, and varied, day-trips. You wouldn't necessarily need or want a car.
I haven't been to Andalucía recently, but I think something similar could be done from Seville (Cordoba, Jerez, Cadiz, Ronda, white villages), but you would almost certainly want a car to get out to the villages. It could still be quite hot in Andalucía in late September. I recommend taking a look at actual day-by-day temperatures from Sep 2018, Sep 2017, etc., on timeanddate.com. I have Iinked to the stats for September 2018, and I see that it hit 100F on the 24th.
Madrid and Barcelona are both large cities. Barcelona is perhaps the more challenging because there are many sights so popular that you will find yourself elbow-to-elbow with other visitors. That may make your husband really uncomfortable.
