Advice on Quick Itinerary

Your plan doesn't optimize the time you have; it minimizes it by having you constantly on trains and buses moving from place to place rather than actually being in places you would enjoy seeing. You are planning to go to four places that very few people would recommend on such a short trip to Spain (Morocco, Tarifa, Gibraltar and Malaga). You are skipping at least two places generally much preferred which are also much more conveniently located with respect to three of your core sights--Toledo and Cordoba.

You are going to have inadequate time everywhere, so you need to dig into a guidebook yourself to select the sights most interesting to you personally. That would always be my advice, but in this case it is especially important. You must surely have had a reason to pack your itinerary with those specific destinations.

Gibraltar and Tarifa cannot be reached by train alone. A rental car will be more efficient than buses if you must go to those places.

You need to figure out your sightseeing targets in Barcelona before you reach Spain. Many of the most popular sights have extremely long ticket lines that you cannot afford to end up in, and some might totally sell out for your time period (though I would hope that wouldn't happen very far in advance). In any case, you'll need to plot out your time in Barcelona very carefully. If you are arriving in Barcelona after an overnight flight, you're likely to be severely jetlagged and possibly also sleep-deprived on your arrival day, so I wouldn't pre-purchase tickets for that day.

There are also one or two key sights in Seville subject to long lines, so buying tickets in advance may be prudent there as well.

Some people also recommend pre-purchase of the ticket to the Palacio Real in Madrid, if you wish to see it.

Rome2rio website gives you transport logistics.
Seat61 dot com provides details on train travel as well as whether rail pass or point to point is best.
How many is 'we' and when are you travelling?

I second acraven. With only 11 days (10 nights) you might want to limit your cities to 3 in order to cut down on travel time which usually takes 1/2 day off your day. Madrid, Barcelona and Sevilla gives you about 3 nights in each with maybe some time for day trips. I would not risk going back to Barcelona the day before I fly home. Consider traveling to Madrid (AVE fast train) the day you land since your bags are already packed and putting all you Barcelona days together at the end. Have fun.

If you really must see a town in Morocco, fly from Barcelona to either Fes or Marrakech for 2 nights, then fly to Sevilla, train to Madrid, train to Barcelona. This reduces your train time. Skip Tarifa, Gibraltar and Malaga. They are 3rd tier places (or lower).

Keep in mind that flying into Spain from the US (?), you are likely to be in a jetlagged haze on the first and possibly the second day as well. Allow 3-4 hours from the plane to your hotel room, depending on lines at passport control, wait time for baggage, and where you are staying in Barcelona. You need to be at the airport for your flight home about 3 hours in advance. You'll have to return to your hotel to pick up your luggage before going to the airport. To me, "leave Barcelona afternoon" means you have an evening flight out.

Thank you all! I really wish we had more time in Spain, or that we could have flown in/out of different cities, or that we didn't have to go to Tarifa/Malaga. Unfortunately, those things are out of our control. There are two of us - me and my niece. We're both experienced travelers, but have never been to Spain before. We always pack extra, extra light to make us nimble and make public transit easier.

We are trying to do everything we can to maximize the time - taking AVE fast train at night when possible, pre-buying tickets online to avoid lines, scheduling sites in "clusters" to avoid transportation delays within each city, etc. I was hoping to get some detailed input on favorite things within each city - ie. favorite places to get tapas, or skip this tourist-y flamenco show and see this other one instead, etc.

@Maria - thank you for the advice on the websites! I will check them out.
@Chani - thank you for the insights into the airport. I will make sure we plan for that.

Licensed private guides are more likely to be Moroccan than Spanish (though there may be some with dual residence). Rick's book has some specific recommendations or you could also try one of the guides who meet the ferry. Be specific about what you want them to show you.

Buses from Seville to Tarifa run 4x/day and take about 3 hours; the first one departs around 9:00 a.m.

There are also buses along the south coast toward your next destinations. Rick's Spain guidebook summarizes the bus companies for each route, or you can try search engines like BusBud.com or just a plain Google search. You might change buses at Algeciras, depending on your preferred schedule. A car gives you more flexibility to set your own route, but isn't strictly necessary, since the buses do exist.

A 3-day Eurail Spain pass for $192 plus 3 seat reservations at about $60 totals $252. If you're willing to reserve train tickets ahead, advance-discount tickets may be cheaper. Places for passholders are also limited if the trains get close to full.

Hi ocnbreezes. I'm planning a very similar itinerary. Will pm you.