1 week in Barcelona with family and then.....

I may have missed it in the post, but could you give us an estimate of how many additional nights you will have after Barcelona? And which city you will fly out of?

Carlos, The number of night after Barcelona is still up in the air. Which I know makes it difficult. My husband is notorious for not committing to a time frame. UGG I would guess a week. Give a few. Honestly sometimes he just needs to see the itinerary laid out for him to go ok book it. I have not booked the air yet. trying to figure out what would make sense and cost. I assume we will fly into Barcelona and leave from depending on wich destination we go. Does this make sense. I know its not helpful to those who plan to the t but at this stage I am trying to be flexible until I have to finalize everything
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If you don't want to deal with tourist crowds, maybe you should reconsider going to Granada, Seville and Cordoba. However, you can fly nonstop to Granda from Barcelona (check Skyscanner) and take a 2h 45m train (www.bahn.com) to Seville and make Seville your home base while you visit Cordoba (45m).
Girona is a 45m train ride from Barcelona and Cadaques is 3h by bus. You can also take a 2h bus from Girona to Cadaques.
When you say alps, do you mean the Pyrenees? You can access this range via ES and FR by car. It's a four hour drive to get there from Girona.
Another option from Barcelona is to fly nonstop to Bilbao and San Sebastian. You can take 1h 15m bus to travel between the two cities.
It's 15m faster to take a train 2h 45 train to Carcassone from Girona than Barcelona. Both require a transfer making this your least convenient place to visit.

In my view these are minimum times for the three major cities in Andalucía. Some people would shave a day off each one, but believe me, you'll have no trouble filling the time. And how energetic are you going to be if it's 95+F? I don't know how easy it will be to find hotels with pools in the cities.

Seville: 4 nights
Cordoba: 3 nights
Granada: 3 nights

If you're interested in both Girona and Cadaques (not to mention points farther north), I highly recommend spending a few nights in Girona rather than repeatedly commuting to that part of Catalunya from Barcelona. Girona is a good base for seeing Figueres (Dali Theatre-Museum, by train), Cadaques (train to Figueres then bus), and Besalu (bus). Or you could drive to the places beyond Girona.

The Basque Country is likely to have very pleasant weather at that time of year, but it takes a good while to get there from Barcelona, and you'll be passing near some very interesting places in the Pyrenees. Hope you'll have enough time to see a lot.

At altitude in the Pyrenees it should be really nice. But the nearby Cerdanya Valley can be blistering hot in the summer. Puigercarda is a pretty hill town, but June-July-August isn't the best time to visit it.

I think you will find Paris and Provence vastly more temperate than Andalucia in the summer in terms of heat, but if you are willing to take that chance more power to you. Ok so for 7 extra nights (best case estimate), I have two potential itinerary recommendations:

"Granada has your Heart":
Fly in to Barcelona
Barcelona (1 week)
Fly low-cost down to
Granada (3 nights)
AVE Train to
Cordoba (2 nights)
AVE Train to
Madrid (2 nights)
Fly out of Madrid

or

"Across the roof of Spain":
Fly in to Barcelona
Barcelona (1 week) - rent car and drive north
drive north to
Girona (2 nights)
turn north-west to
Besalú (1 night)
drive west stopping at Ripoll monastery, cont. to
Ribes de Freser (1 night) - day trip to Vall de Nuria (Pyrenees)
cont. west to
Puigcerdà (2 nights) - explore Cerdanya valley
turn back south to
Vic (1 night) - day trip to medieval cliffside village of Rupit
Drive back to Barcelona, return car, and fly out

Or fly down to Granada from Barcelona then 1-2 nights there. Then bus to Seville for 3 nights. Either train up to Madrid for flight home or try to find something out of Seville.