How exciting! You and your family will have a beautiful experience wherever you decide to go in Spain.
My vote based on your thoughts, would be to start in Barcelona. Then explore Sevilla (or Toledo, Granada or Cordoba if you prefer) and see Madrid before flying out of that city.
I've spent Christmas/New Years in Barcelona 5 years ago and really enjoyed being there. Last year for Christmas/New Year's, we celebrated in Madrid and I flew out of Barcelona. I felt it was easier to get around on NYE in Barcelona. Luckily we were staying in a great/central location in Madrid on NYE, so we saw fireworks easily and had a great holiday. Both cities are wonderful and have their unique charm. I found the NYE celebrations more festive in Madrid (loved the fireworks and the energy that night)! I also appreciated how easily it was to get from Madrid to Sevilla, which was by far the best part of my trip. Sevilla is my favorite city that I ever experienced and I had a blast exploring this magical, unique place. There are quite a few celebrations after the Christmas/New Year's in Sevilla (Regalos de Navidad para los ninos) so it feels like an extended holidays (which I imagine would be special to your family).
Weather wise, it was incredibly pleasant and often sunny in all cities mentioned during my visits. A sweater or light jacket was all I needed at night. Barcelona, Madrid and Sevilla are all extremely family friendly.
Have fun and all the best! You'll have a wonderful time.