10 year, I was also going to suggest calling AA directly. Their number for FF is 1-800-882-8880. I have had their wonderful reservationists go out of the way to help with complex tickets of all kinds. Also, they can put certain tickets on hold for a limited time. Don't bother with the website except for basic information.

Here's my 2 cents for what they're worth:

I would stick with the original plan of staying 2 nights in Toledo. I'm not a bit fan of Madrid and I love to visit Toledo and spend the night there especially after a transatlantic flight. A nice place to get a little rested and a much different city after the day trippers have left.

I wouldn't bother with a car until after Sevilla. It's an easy train/bus from Madrid to Toledo and return. From Madrid you can easily get the AVE to Sevilla via Cordoba. I'd do Cordoba as a daytrip and definately spend 3 nights in Sevilla at least. It's a charming, romantic, beautiful city. Another thought, about 45 minutes away, is the small town of Carmona. They have a wonderful parador. You definately won't need a car in Sevilla. I'd cut a couple of days from the Algarve and from Sevilla head to Arcos and Ronda, visiting the white village towns along the way (renting a car at this point). Although you'd be cutting down on your "quiet" beach time, these wouldn't be rigorous days - just laid back driving along the route stopping on a whim. You could even visit the sherry town of Jerez de la Frontera on the way from Sevilla to Arcos - about 1/2 way in the middle 45 minutes from both Sevilla and Arcos.

Personally, if you've never visited the Alhambra, I'd be tempted to cut out the Algarve and head from Ronda to Granada, but this is your call AND your vacation.

Just my opinion and won't be insulted whatever you decide! Hope you have a great trip, happy planning, and keep the questions coming!