Staying in Seville vs Cadiz next January

I’ll assume you will have a rental car. Since you’re visiting cousins stationed in Rota, why not stay there. You can take the ferry to Cadiz from the port area in Rota. A really nice hotel in town the the Duque de Najera, right by the port. From there, Puerto de Santa Maria and Jerez are nearby, and Sevilla is an easy, just over an hour drive away. Arcos de la Frontera is about 45 minutes away and Córdoba about 1.5 hours away. To me, Cadiz is only worth a few hours visit, especially that time of year. While there’s not a lot going on in Rota that time of year, you’d be close to your relatives. From the Duque de Najera hotel to the base gate, it’s about a 15 minutes walk. Personally, I’d skip the Morocco day trip and opt for Arcos de la Frontera and the white towns, and Ronda instead. If you plan to spend more than a minimum amount of time with your cousins, then stay in Rota. If you only plan a quick visit with them, then use Sevilla as a base. When I was stationed there years ago, I enjoyed taking family around to see the sights when they visited.

You only have 3 days and a few hours, part of which will be dedicated to visiting family. Please don't spend one of those precious days going to Tangier. You could easily spend all your time in Seville, much less the various local options already suggested. Plus there's Cordoba, which I would choose instead of the white villages if you could see it in transit between Seville and Madrid.

we could spend the majority of the day exploring Seville 1/5.

I wouldn't plan on that. viamichelin.com estimates the driving time from Sevilla's center to the airport at 5.5 hours. For an international flight, it's recommended to arrive at least 2 hours, preferably 3, before the flight. Even if your flight's at 10 pm, that means leaving Sevilla no later than 2.30 pm and that's with no cushion for delays, traffic and wrong turns. The fastest train from Sevilla to Madrid Atocha station is 2.5 hours. You'd still have to get to the airport by bus, taxi or metro/cercanias. The trip on the cercanias takes about 35 minutes, the trains run about every 30 minutes.

You've been advised several times in previous posts not to go to Tangier. I guess there's no point in repeating it, but do check the ferry schedule to make sure it's possible to do a day trip. viamichelin.com estimates driving time from Sevilla to Tarifa at 2.5 hours, from Cadiz 1.5 hours.

Chani--we do not fly out of Madrid on the 5th. We'll take the train there that evening, which is listed at about a 2.5 hour ride, then we will be in Madrid until 1/7 when we fly out. So we would not be needing to rush out of Seville to get to Madrid at any specific time that day.

Our group is all very interested in Tangier and would prefer to go there over some of the other places people have suggested instead. We have family friends who just recently did the day trip to Tangier from Seville and highly reccomended it.