Gibraltar

It's interesting as all get out. However, if that's the only thing you're going to see when you go south, it's probably not worth the time or the money. There's plenty to see closer to Madrid.

I have no idea if you can get down there and back in a day by public transportation. It's a good seven or eight hour drive one-way.

It would be a very long day and expensive. Two and half hours train to Seville, rent a car and drive two and a half more hours to Gibraltar. You might consider staying in Seville for a couple days instead of Madrid for a whole week. Although Madrid is great and you can easily will a week with that city plus close day trips.

We enjoyed our day visit to Gibraltar in April, but only went there because we were already in the south. There are a lot better things to do and see in Madrid and Barcelona. I don't feel it would be worth your time and effort just to see Gibraltar.

Gib is a long haul from either of your base cities. I took the overnight train form Barcelona to Grenada for the Alhambra and then a regional train (brutal) down to Algeciras for Gib and Tangier. It is a long haul down there and while Gibraltar is well worth a visit, in your situation I'd pass it up until you have a reason to tour the south of Spain (and there are plenty of good reasons to do just that).