Andalucía is sort of the classic Spain we all picture (until we've been to Barcelona, anyway), so it's understandable that your family wants to stick with that plan. And it may be the right thing for you to do, because there is no traveler as unhappy as one who is not where he wants to be (which in his imagination is a lot better than the current reality).
But indulge me while I give my rather standard explanation of how traveling in Europe differs from the way you live at home. When it's super-hot at home, I'm betting you mostly go from your air-conditioned house to your air-conditioned car to an air-conditioned school/workplace/store/movie theatre, etc. That's not the way it is in Europe. You will be outdoors a lot, as Chani pointed out. I think you will find that some small cafes, shops and restaurants are not air conditioned. This may actually be less of a problem in southern Spain than farther north because of the extreme heat, but it was issue when I visited southern Italy, and I think you will face it in Spain as well. Even museums may not have a/c if their holdings are things like sculpture rather than paintings and works on paper. Very old churches are sometimes your best hope of finding a cool spot; those thick stone walls are very protective.
You will initially be surprised at how many Spanish businesses close for 3 or 4 hours in the early afternoon--because of the heat, and because they are sane. While you can soldier on through a day of high heat, you won't make it through your entire trip in decent shape if you ignore tough conditions of the sort I fear you will face. Assume that you will not just want, but need, to retreat to your hotel room for a while to cool off, ideally every day, but in reality that will only be possible on days when you aren't making out-of-town day-trips.
Establish a schedule that has you out sightseeing early in the morning while it is still pleasant. That will make up for the time lost during the hottest part of the day. Although you may be out and about before your first planned sight opens, it will be a great opportunity to enjoy the atmosphere and some relatively quiet time in historic surroundings. It will stay light very late, and Spaniards have dinner after 9 PM or 10 PM, so you'll be out during the somewhat cooler time in the evening as well. This is another reason you'll need to crash during the day.
Be sure your packing list takes into account the expected high temperatures: hats with brims for everyone (ideally, vented so they keep you cooler) and plenty of sunscreen. The sun will reflect off light-colored stone and white-washed buildings, so you can get sunburn on your face even while wearing a brimmed hat. Leave the standard (heavy) blue jeans at home. Check your guide book for references to churches that require women to cover their shoulders and all to have their legs covered to the knee or some other point. There may be no such places where you are going, or there may be several. I have found a Kool Tie to be somewhat helpful in high heat. There are competing products, and there are other sources.
I trust it goes without saying that you need to read hotel/apartment reviews very carefully before booking, paying particular attention to comments about the quality of the air conditioning. I would expect that not to be an issue where you are headed, but you need to make sure. Read a bunch of current reviews, but also scroll back through all the winter and fall reviews to find the ones where last year's a/c problems would be discussed.
I don't know how widely available pools are at Andalucian lodgings, but I imagine access to a pool would contribute mightily to family harmony.