Caveat: I hate cold, wet weather and have never traveled to Europe in March. I did go to Andalucia in early April 2019 and was pleased with the weather except for two chilly, wet days in northern Andalucia at the beginning of the trip.
What city/cities are you flying into and out of? On a trip of this length, that would majorly affect the itinerary I would choose.
It appears that you have just 7 full days on the ground in Spain. The arrival day (maybe also your first full day) will probably be significantly affected by jetlag. I would definitely not want to deal with three different hotels during that time and would be inclined to choose one base worthy of multiple days of sightseeing that also offers good side-trip possibilities. Personally, I would not be willing to insert a flight in the middle of so short a trip, nor would I be willing to give up a huge chunk of my vacation to shift between two distant cities.
Weather-wise, Andalucia or the east coast would be my preference; the center of the country could still be quite chilly at that time of year. I haven't researched March weather in Spain, but I wonder what it's like at that time of year in Mallorca; it might also be suitable. Palma has some interesting architecture (including modernista buildings), and there are lots of scenic side trips and smaller towns to explore. It may not have enough big-city-quality museums for you, though.
Barcelona works, or a combination of Barcelona and Girona. Either would allow a side-trip to Figueres for the Dali Theatre-Museum (a quicker trip from Girona). Girona is a charming, historic smaller city that should appeal to your daughter. Figueres, unfortunately, is pretty much all about the Dali museum. The medieval town of Besalu is accessible by bus from Barcelona or, more quickly, from Girona. There are many other options in Catalunya, but you are almost certain to have a hard time dragging yourselves away from Barcelona. If you stay somewhere like the Gracia neighborhood, your hotel will not feel as if it's in a large city.
The weather would probably be warmest in the south; you could spend the entire time in Seville and take a few side trips, but it's a big, bustling city and your daughter would probably prefer to have some nights in a quieter environment. You could combine stays in Seville and Cordoba or Seville and Granada (maybe squeezing in a day trip from Seville to Cordoba). This area is more about historic sites and charming mudejar architecture than art museums. There are attractive side trips to small towns from both Seville (including Carmona) and Granada (including Priego de Cordoba). Granada is at altitude so is likely to be chillier than Seville and Cordoba.
I like both Valencia and Malaga, but they don't have as many major sights as Barcelona or Seville. Given the time of year, I wouldn't prioritize being on the coast to the extent of choosing a secondary city like Valencia or Malaga. I am not a beach person, but I don't think March would be beach season anywhere in Spain unless you just want to walk on the sand.