I love Toledo. It has more than a full day's worth of sights. I wouldn't go there for just my first night unless I planned to take quite a late train back to Madrid on Day 2, giving me practically the entire day in Toledo. Otherwise, from my perspective you're just churning hotels for no real reason. If I only had Night 1 for Toledo, I'd just go to my Madrid hotel, drop off my bags, and walk around (in the heat, unfortunately). I went to the Botanical Garden on Day 1 myself, but that was on May 16, and it might not much appeal to your children. Retiro Park might be a better choice, and it's free. San Miguel Market is a good place to graze on tapas, cups of cut-up fruit, and the like if you have the munchies before lunch starts at 2 PM.
Take a look at the wunderground link in my earlier post. It will show you temperatures for August 2016 in Seville. You can use the pull-down boxes to change to 2017, 2015, etc.
It's not just an issue of whether Andalucia will be hotter than Florida; you need to consider how you'll be spending your time. Unless you have an outdoor job in Florida, you probably basically move from your air-conditioned home to your air-conditioned car to your air-conditioned workplace (or an air-conditioned store, etc.). That is not what a tourist does, and you'll find that in Europe, not every small establishment is air-conditioned. Small bars, cafes and shops may not be. Museums that don't hold paintings and works on paper may not have a/c. Not being able to escape the heat is really draining. And it's not as if you're likely to have pleasant temperatures in Madrid and Barcelona, either. So ask yourself whether you're up for 10 or 11 days of probably-unremitting heat, and whether you'll be happy if 3 of them hit 100F.
If this is likely to be your last visit to Spain, it's right to balance that against the weather situation. In that case, you may decide to proceed. Be sure you select conveniently-located hotels so you can take a mid-day break in your air-conditioned room if you need to (and you will). Plan to get up and out of the hotel very early to start your day. It's not a natural thing to do for an American in a country that sits down to dinner at 10 PM or later, but it will buy you a couple of not-dreadful sightseeing hours in the morning.
I've found wearing a Kool-Tie makes me keel a bit better in the heat by keeping my neck cool. I've linked to Amazon, Kool-Ties and apparently-similar products are also available from other sources.
Incidentally, there are places in northern Spain that are almost certain to have very pleasant temperatures in August; they just aren't the places most people go on their first trip to Spain.